College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.6 - Rational Exponents - R.6 Exercises - Page 57: 66



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the laws of exponents to simplify the given expression, $ \dfrac{(r^{1/5}s^{2/3})^{15}}{r^2} .$ $\bf{\text{Solution Details:}}$ Using the extended Power Rule of the laws of exponents which is given by $\left( x^my^n \right)^p=x^{mp}y^{np},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{r^{\frac{1}{5}\cdot{15}}s^{\frac{2}{3}\cdot{15}}}{r^2} \\\\= \dfrac{r^{3}s^{10}}{r^2} .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} r^{3-2}s^{10} \\\\ r^{1}s^{10} \\\\ rs^{10} .\end{array}
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