Algebra and Trigonometry (1st Edition)

Chapter 1

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A natural number is a positive integer. The number... more

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; It is observed that the Length of matte is  and... more

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; Break the term such that a common factor can ... more

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is an irrational number because it has neither a ... more

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The order of operations is a sequence of solving a... more

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As per the associative property, during ... more

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14 ; With the help of the order of operations, ... more

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-6 ; The given equation can be simplified with the... more

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10 ; Simplify the given equation with the help of ... more

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-2 ; Use the order of operations to simplify the ... more

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12 ; Simplify the given equation with the help of ... more

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-9 ; Simplify the given equation with the help of ... more

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5 ; Simplify the given equation with the help of ... more

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9 ; Simplify the given equation using the order of... more

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27 ; Simplify the given equation with the help of ... more

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-2 ; Simplify the given equation with the help of ... more

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16 ; Simplify the given equation with the help of ... more

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4 ; Simplify the given equation with the help of ... more

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216 ; Apply the quotient rule of exponents... more

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; Apply the product rule of exponents ; Use the ... more

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; Apply the power rule of exponents to simplify ... more

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; The  term contains the same base raised to ... more

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; The numerator and denominator contain the same ... more

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; Count the number of zeroes.Move 5 places to the... more

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; Count the number of zeroes.Move the decimal to ... more

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16,000,000,000 ; Move the decimal 10 places to the... more

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0.0000000098 ; Move the decimal 9 digits to the ... more

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; Apply the product rule of exponents and ... more

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; Apply the quotient rule of exponents . Note ... more

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; Apply the power of product rule . Note that , ... more

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; Apply the power rule of exponents  . ; Simplify... more

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; Represent the expression in the form of a ... more

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; Apply the power of the product rule . Note that... more

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; Recall that the zero exponential rule states ... more

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1 ; Apply the power of the exponent rule . Note ... more

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; Follow the steps below to obtain the result:... more

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; Apply the power rule of exponents to simplify. ... more

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; Apply the power rule of exponents. Note that ... more

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; Assume .Simplify using the power law as follows... more

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25 ; Assume .Rearrange it as follows: ; more

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; Assume .Simplify it using . ; more

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; Assume .Simplify it using . ; more

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; Assume .Simplify it using the power law . ; more

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; Assume .Simplify it using the multiplication ... more

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; Assume .Simplify it using and .     ; more

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; Assume .Simplify it using . ; more

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; Assume the travel distance at any instant to be... more

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; The standard unit of thickness is the same as ... more

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; In scientific notation, the first number has to... more

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; While writing 1,099,500,000,000 in a scientific... more

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; The standard notation is the normal manner of ... more

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; The standard notation is the normal manner of ... more

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; Simplify it using the number of zeros in a ... more

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; Input the given function in the graphic utility... more

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; Input the given function in the graphic utility... more

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  ; Assume, Simplify it using and ; more

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; Assume Use and simplify it  ; more

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  ; Assume the given expression to be p.Use to ... more

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Commutative property ; The total change in the jar... more

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; To construct an equation, covert the statements... more

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; Consider the equation . Solve the equation for... more

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An inverse property of addition. ; When the sum of... more

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1.56 ; Enter the equation in the graphic ... more

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68.4 ; Enter the equation in the graphing ... more

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0 ; All the positive integers and 0 are members of... more

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A rational number is of the form , where and are... more

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When an irrational number is multiplied with a ... more

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Evaluate the expression, 38 is not a perfect ... more

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Evaluate the expression, 3 is a rational number... more

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Rational number ; Whole numbers are a subset of ... more

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Distributive property ; The distributive property ... more

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; Write the scientific notation of the number of ... more

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No, is equal to 8 and is equal to 9. ; The ... more

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When numbers with the same or different exponents ... more

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The purpose of scientific notation is to make ... more

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The negative exponent reciprocals the given number... more

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81 ; Simplify the given expression by multiplying ... more

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; Use the rule of negative exponent.The negative ... more

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243 ; Use the product rule of exponents which ... more

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64 ; Use the quotient rule of exponent, i.e, and ... more

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; Use the power rule of exponents, i.e., . ; Use ... more

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1 ; Use the zero rule of exponent, i.e., . ; more

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; Use the quotient rule of exponent, that is, , ... more

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; Use the product rule of exponent, that is, ; ... more

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1 ; Use the power rule of exponent, i.e., . ; more

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; Use the quotient rule of exponent, that is... more

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; Use the product rule of exponent, that is, . ; ... more

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; Use the quotient rule of exponent, i.e., . ; more

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; Use the product rule of exponent, that is, . ; ... more

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; Use the power rule of exponents, that is, . ; ... more

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; Product rule for the exponents is defined as . ... more

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; Consider the properties of exponents as follows... more

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; A number is said to be expressed in a ... more

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; A number is said to be expressed in scientific ... more

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16,000,000,000 ; A number in a scientific notation... more

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; A number in a scientific notation can be ... more

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. ; The negative rule of exponents states that any... more

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. ; The negative rule of exponents states that for... more

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. ; The power of a product rule of exponents says ... more

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. ; The power of quotient rule of exponents is ... more

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. ; The given expression is used to find the ... more

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; The expression contains a term raised to the ... more

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; In the expression , the denominator is raised ... more

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1 ; The expression contains two terms of ; since ... more

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; Apply the negative rule of exponents to all the... more

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; The given expression contains the product of ... more

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; Apply the power rule of exponents to the term ... more

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; The expression is a fraction raised to a ... more

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25 ; The denominator of the expression contains a... more

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; Apply the power of a product rule of exponents ... more

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; Employ the negative exponent rule to take out ... more

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; Simplify the term in the bracket by using the ... more

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; Use the negative exponent rule to consider the ... more

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; Use the quotient rule to simplify the ... more

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; Simplify the bracket by considering the term ... more

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; Get the required value by moving the decimal 6 ... more

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; To write the number in standard notation, the ... more

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; To get the required value, move the decimal to ... more

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; Get the required value by shifting the decimal ... more

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; To get the required value, shift the decimal ... more

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; To get the required value, shift the decimal ... more

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; To get the required value shift the decimal ... more

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; Input the given function in the graphic utility... more

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  ; Input the given function in the graphic ... more

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; Use the negative rule and simplify the terms in... more

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; Simplify the expression in the bracket using ... more

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; Use the negative rule to simplify the ... more

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; Use the negative rule to simplify the two ... more

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; Use the negative rule to remove the negative ... more

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602214130000000000000000 ; Get the required value ... more

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The Planck's constant in the standard notation is ... more

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; Split the terms in the given expression to ... more

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; The product rule for square roots states that... more

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; Evaluate the square roots in the numerator and ... more

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; Simplify the given expression . ; more

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; Simplify the given expression . ; more

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0 ; Simplify the given expression using the ... more

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; Simplify the given expression using the common... more

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; Simplify the given expression . ; more

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243 ; Apply the power rule for the exponents to ... more

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; Simplify the given expression . ; more

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; Simplify the given expression . ; more

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A radical without an index represents the square ... more

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Second order ; According to the order of ... more

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Principal square root will be the positive square ... more

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No; The square of a number is never negative. ; ... more

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16 ; According to product rule of square roots is ... more

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4 ; According to product rule of square roots is ... more

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10 ; According to product rule of square roots is ... more

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6 ; As as and as Now, use these values and ... more

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14 ; The value of is equal to 196. So, equals 14... more

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1 ; The value of is equal to 1. So, equals 1. ; more

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; According to the product rule of square roots, ... more

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; According to the product rule of square roots, ... more

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; According to the product rule of square roots, ... more

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; Use the product rule and write as then ... more

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25 ; Solve the square roots by writing 169 as and... more

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; First, split the radicals into numerator and ... more

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; Follow the steps below to simplify the ... more

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; Use the property and write as the product of ... more

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; Use the product rule and write as the product ... more

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; To simplify Write 45 as the product of 9 and 5 ... more

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; Factor the term 150 as and split the radicals ... more

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; To simplify the expression perform the ... more

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; To simplify the expression perform the ... more

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; To simplify the expression perform the ... more

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; To simplify the expression perform the ... more

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; To simplify the expression:Apply the quotient ... more

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; To simplify the expression:Apply the quotient ... more

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; To simplify the expression multiply the ... more

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; To simplify the expression: Multiply the ... more

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2 ; To simplify the expression:Apply the rule ... more

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; To simplify the expression:Rewrite the term 128... more

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; To simplify the expression:Apply radical rule ... more

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False ; To simplify the expression:The roots are ... more

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; Add similar elements ; more

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; Apply radical rule , assuming Apply exponent ... more

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; Apply radical rule , assuming Apply radical ... more

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; Apply radical rule , assuming ; more

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; Apply radical rule , assuming Apply radical ... more

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17 ; Use the square root of 289 which is ; more

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; use this to solve the expression . ; more

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; Simplify the expression using the distributive ... more

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; The exponential formula required to solve the ... more

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; Simplify the given expression, , using the ... more

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; In the given expression, , simplify and ... more

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; In the given expression , use the formula to ... more

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; In the given expression , use the formula to ... more

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; In the given expression, , use the formula to ... more

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;  Factorize and simplify the given exponential ... more

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; Simplify the given expression using the ... more

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; Simplify the given expression using the ... more

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;  Simplify, the given expression using the ... more

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; Simplify the given expression , using the ... more

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; Use the formulae to simplify the given ... more

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;  Simplify the given expression , using the ... more

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; Formulae used:  Simplify the given expression ... more

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; Simplify the given expression using . ; ... more

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; Simplify the given expression using the ... more

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; Simplify the given expression using the ... more

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; Factorize the given expression using the ... more

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; Simplify the given expression using the ... more

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; Simplify the given expression using the ... more

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; Factorize the function and then evaluate for ... more

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4z ; Initially, factorize the function partially ... more

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4 ; Initially, factorize the given number to find ... more

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500 ; The length of the guy wire according to the ... more

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; First factorize and then subtract the equation... more

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; First, simplify both the numerator and the ... more

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-28 ; First, convert the power of both the ... more

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; Factorize both the numerator and the ... more

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; Simplify the rational function, multiply both ... more

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; Factorize the function and eliminate the factor... more

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; Factorize and eliminate the  actor of one from ... more

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; Individually factorize both the numerator and ... more

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 Degree is 6, the leading term is , and the ... more

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; To find the sum, combine the like terms of both... more

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; Initially, open the parentheses and subtract ... more

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; Apply the distributive property and simplify to... more

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; Initially, find the product of the first terms ... more

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; Initially square the first and last terms of ... more

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; Initially, square the first term.  ;   ; Then, ... more

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; First multiply the given polynomial using the ... more

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When a polynomial is written in the standard form... more

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When two binomials have the same terms but the ... more

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The four basic steps used for the multiplication ... more

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A trinomial can have all the terms of power one, ... more

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2 ; Consider the polynomial , the second term is ... more

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3 ; Consider the polynomial , the first term is ... more

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8 ; Consider the polynomial , the first term is ... more

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3 ; Consider the polynomial , the third term is ... more

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2 ; Consider the polynomial , the first term is ... more

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5 ; Consider the polynomial , the second term is ... more

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; Remove the parentheses and change the signs of ... more

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; Remove the parentheses and rearrange the terms... more

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; Remove the parentheses and change the signs of ... more

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; Remove the parentheses and rearrange the terms... more

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; Remove the parentheses and rearrange the terms... more

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; Remove the parentheses and rearrange the terms... more

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; Open the first parentheses using the ... more

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; Use the distributive property to open the first... more

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; Open the first parentheses using the ... more

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; Open the first parentheses using the ... more

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; To simplify ,first multiply by and by -9. ... more

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; To simplify ,first multiply by , and multiply... more

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; To find the product of , first multiply by ... more

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; To expand the binomial ,using the formulae ;, ... more

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; To expand the binomial expression ,using the ... more

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; To expand the binomial expression ,use the ... more

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; To expand the binomial expression , use the ... more

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; To expand the binomial expression , use the ... more

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; To expand the binomial expression , use the ... more

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; To expand the binomial , use the formulae , ... more

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; Apply the square formula for the sum and ... more

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; Use the difference of square formula to ... more

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; To simplify , multiply by and multiply by 6... more

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; To simplify , multiply by and multiply by -2... more

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; To simplify , multiply by 4 and multiply by... more

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; To simplify , multiply by and multiply by -7... more

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; To simplify , multiply by and multiply by 10... more

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; To simplify , multiply by and multiply by -1... more

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; To simplify , first multiply by and multiply... more

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; To simplify , first multiply by , by , and ... more

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; Use the distributive property to simplify the ... more

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; Use the distributive property to simplify the ... more

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; Use the distributive property   to simplify the... more

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; Use the distributive property to simplify the ... more

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; Use the distributive property to simplify the ... more

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; Use the distributive property to simplify the ... more

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; Use the expression and then apply the ... more

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; Use the distributive property to evaluate the ... more

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; Use the distributive property to evaluate the ... more

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; Use the distributive property to evaluate the ... more

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; Use the distributive property to simplify the ... more

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; Use the distributive property to evaluate the ... more

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; To find the area, multiply the first terms,  ... more

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; Simplify the area of floor using the formula... more

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; Expand the square using the formula . ; Use the... more

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; Multiply the binomials and using the ... more

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; Use the distribution rule to evaluate the ... more

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; The GCF of a polynomial  is the greatest ... more

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; To factorize , evaluate the two numbers with a ... more

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; Factorize 9 into two numbers in such a way that... more

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; The first and the last elements of the ... more

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; The terms in the expression , that is, and 100... more

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; As can be written as , express as the sum of ... more

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; As can be written as and 125 can be written ... more

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; Since , common out from the expression . ; Use... more

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No  ; If the terms of a polynomial do not have a ... more

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The expression of the form of sum of the cubic ... more

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A trinomial of the form can be factorized using ... more

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; GCF of a polynomial is the largest value that ... more

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; GCF of a polynomial is the largest value that ... more

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; Greatest common factor of a polynomial is the ... more

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; The greatest common factor of a polynomial is ... more

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; The greatest common factor of a polynomial is ... more

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  ; The greatest common factor of a polynomial is ... more

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; To factorize , two numbers are required such ... more

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; To factorize , two numbers are required; ... more

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; To factorize , two numbers are required; ... more

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; To factorize , two numbers are required; ... more

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; To factorize , two numbers are required; ... more

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; To factorize , two numbers are required such ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; Solve using the grouping method. The standard ... more

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; It is known that is equal to , and 100 is ... more

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; It is known that is equal to , and 196 is equal... more

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; It is known that is equal to , and 169 is ... more

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; It is known that is equal to , and 9 is equal ... more

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. ; It is known that is equal to and 81 is equal... more

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. ; It is known that is equal to and 121 is ... more

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. ; It is known that is equal to and is equal ... more

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; Check if both the quadratic term and constant ... more

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. ; Check if both the quadratic term and constant ... more

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. ; Check if both the quadratic term and constant ... more

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. ; Check if both the quadratic term and constant ... more

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. ; Check if both the quadratic term and constant ... more

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. ; Check if both the quadratic term and constant ... more

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; On comparison with a trinomial of the form , it... more

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; It is known that . Hence, it is observed that ... more

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; Polynomial expression is can be written as as... more

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; Polynomial expression is can be written as as... more

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;  The polynomial expression can be written as ... more

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; The polynomial expression can also be written ... more

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; The polynomial expression can be written as ... more

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; The polynomial expression can be written as . ... more

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; To solve polynomials with negative exponents, ... more

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; To solve polynomials with negative exponents, ... more

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; To solve polynomials with negative exponents, ... more

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; To solve polynomials with fractional exponents... more

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; It is known that, to solve the polynomials with... more

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; It is known that to solve polynomials with ... more

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;  It is known that to solve polynomials with ... more

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; It is observed that the area of the rectangle ... more

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; It is observed that the area of the base of the... more

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; To find the length of the fountain:The ... more

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; It is known that . Hence the given expression ... more

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; In the polynomial expression , let . Then, the ... more

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; can be written as and 256 can be written as ... more

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; can be written as and can be written as Hence, ... more

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; To solve the polynomials with negative ... more

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; The common factor is taken from and Here, the ... more

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; The denominator is of the form of the ... more

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; The numerator and the denominator are factored ... more

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1 ; To divide 2 rational expressions, the second ... more

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; The least common denominator is the smallest ... more

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; The least common denominator is the smallest ... more

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The factoring allows equal factors to be cancelled... more

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The denominators of two rational expressions are ... more

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True as the Lowest Common Denominator is used to ... more

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; To simplify rational expressions, the numerator... more

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; To simplify rational expressions, the numerator... more

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; To simplify rational expressions, the numerator... more

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; To simplify rational expressions, the numerator... more

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; To simplify rational expressions the numerator ... more

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; To simplify rational expressions, the numerator... more

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; To simplify rational expressions the numerator ... more

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; To simplify rational expressions the numerator ... more

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. ; To simplify the rational expression follow ... more

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. ; To simplify the rational expression , follow ... more

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. ; Simplify the expression by factoring.To ... more

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. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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1 ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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1. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression follow ... more

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. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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. ; To simplify the rational expression , follow ... more

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1 ; To simplify the rational expression follow ... more

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. ; To simplify the rational expression , follow ... more

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; Simplify the numerator of the first fraction ... more

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; To simplify the rational expression follow the... more

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. ; Since the division of the first rational ... more

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. ; To add the given rational expression, find the... more

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. ; First, cancel the common factor 2 from the ... more

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; First, find the same denominator for each ... more

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. ; Since the least common divisor of the given ... more

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. ; To add the given rational expressions, first ... more

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. ; To subtract the given rational expressions, ... more

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. ; To add the given rational expressions, first ... more

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. ; To subtract the given rational expressions, ... more

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. ; To add the given rational expressions, first ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; Follow the steps below to convert the ... more

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. ; To simplify the given rational expression, ... more

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. ; Follow the steps below to divide   by .... more

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. ; Follow the steps below to divide   by .... more

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. ; Use the grouping method factor to solve . Here... more

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. ; Change the division sign to multiplication by ... more

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. ; Rationalize the expression to make the ... more

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4. ; Change the sign from division to ... more

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-5 ; With two or more operations in a single ... more

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6 ; When there are two or more operations in a ... more

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53 ; When there are two or more operations in a ... more

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; Subtract 9 from both sides of the equation... more

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Group 1: Rational number,  Group 2: Irrational ... more

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64 ; Use the product rule of exponent that states ... more

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16 ; Use the quotient rule of exponent that states... more

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. ; Use power of a quotient rule to simplify . ; ... more

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; Use the product rule of exponent which states ... more

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; Use the power rule of the exponent, that is,  ... more

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; Simplify the expression using the zero ... more

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; The negative rule of exponent:If is a real ... more

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a ; The negative rule of exponents:If is a real ... more

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0.0000021314 ; In a scientific notation, the ... more

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; In scientific notation, a number is written in ... more

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11 ; Convert 121 into the factors of 11.After that... more

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14 ; The given number, 196 is a perfect square of ... more

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19 ; Convert 361 into the factors of 19.After that... more

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; If and are positive real numbers, then .To ... more

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; If and are positive real numbers, then . To ... more

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; If and are positive real numbers, then .... more

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; If and are positive real numbers, then . ... more

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; The given expression is . If and are positive... more

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; To remove the radical from the denominator,  ... more

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; If the terms have the same radicals, then add ... more

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; If the terms have the same radicals, then ... more

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-3 ; To find the value of , convert -243 in five ... more

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; If and are positive real numbers, then .Use ... more

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; To simplify:Remove the parentheses.Group the ... more

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; Distributive property: If , and are real ... more

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; Remove the parentheses.Group the like terms ... more

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; Use the distributive property to open the ... more

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; Use the distributive property to open the ... more

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; Use the distributive property to open the ... more

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; Use the distributive property to open the ... more

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; Use the distributive property to open the ... more

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; The greatest common factor of the constants in... more

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; The greatest common factor of the constants in... more

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; The greatest common factor of the constants in... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form and ... more

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; Rewrite the given expression in the form and ... more

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; Rewrite the given expression in the form , and ... more

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; Rewrite the given expression in the form and ... more

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; To simplify the expression , factor out the ... more

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; Factor out the term from the given expression ... more

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; To simplify the expression , factor out the ... more

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; To evaluate the rational expression , factorize... more

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; For the expression , use the identity to ... more

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; Factorize the numerator and denominator as the ... more

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; To evaluate the rational expression, apply ... more

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-13 is a whole number, whereas is an irrational ... more

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-2 ; Replace each by 2 in the function equation ... more

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10 ; Replace each by 1 in the function expression... more

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3114500 ; Write in the standard form.Hence ... more

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; Find the number of digits in 0.0000000212.There... more

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16 ; Simplify the parenthesis first , and simplify... more

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9 ; Two exponents are multiplied using the ... more

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; Use the power rule of exponent, to simplify ... more

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; In the expression , simplify the denominator ... more

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; If the power of any value is 0, then it is ... more

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21 ; It is known that the square root of a value ... more

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; First, write 490 as the product of 49 and 10. ... more

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; The square of 3 is 9, and the square of 4 is 16... more

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; Use the property , and rationalize the ... more

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; In the expression , write as the product of , ... more

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; To simplify the expression, , rewrite -8 as the... more

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; Remove the parenthesis using the distributive ... more

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; Using distributive property, multiply each term... more

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; Using distributive property, multiply each term... more

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; First, rewrite 16 as the square of 4 and 81 as ... more

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; First, rewrite 36 as the square of 6 and as . ... more

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; First, rewrite 27 as the cube of 3 and 1331 as ... more

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; The expression is given as  Simplifying the ... more

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