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Simplify each expression, if possible. $$ \frac{\…

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105 Problem 106 Problem 107 Problem 108 Problem 109 Problem 110 Problem 111 Problem 112 Problem 113 Problem 114 Problem 115 Problem 116 Problem 117 Problem 118 Problem 119 Problem 120 Problem 121 Problem 122 Problem 123 Problem 124 Problem 125 Problem 126 Problem 127 Problem 128 Problem 129 Problem 130 Problem 131 Problem 132

Problem 106 Hard Difficulty

Simplify each expression, if possible.
$$
\left(\frac{2 s^{2}}{3 t^{5}}\right)^{5}
$$

Answer

$\frac{32 s^{10}}{243 t^{25}}$

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Algebra

Elementary and Intermediate Algebra 5th

Chapter 5

Exponents and Polynomials

Section 1

Rules for Exponents

Related Topics

Exponents and Polynomials

Polynomials

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Video Transcript

We need to simplify the given expression. The given expression is shown here. We know that the power of quotient rule for exponents states that if a patient x by y is raised to power n, then it can be written as x, power, n red by y power e n. So let us apply the power of quotient rule in the given expression. We get 2 s square raised to power 5 by 3 p power 5 raised to power 5. We know that the power of product rule for exponents states that if a product x y is raised to cover in then it can be written as x, power n into y cover n, so raising each factor of the product to power 5. We get 2 power. 5 and s square raised to power 53 power 5 and t power 5 raised to power 5. So, on simplifying this we get the value of 2 power. 5 is 32 point. We know that the power rule for exponents states that if a power is raised to power n, it can be written as a power into n so keeping the base. Yes, let us multiply the exponents 2 into 5 and the value of 3 power. 5 is 243 and keeping the base. Let us multiply 5 into 5 on simplifying this. We get 32 s. Power 10 divided by 243 t power, 25 pothe solution;

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Alan S. Tussy, R. David Gustafson

Elementary and Intermediate Algebra 5th

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