Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set: 55

Answer

$\dfrac{1}{\sqrt[4]{8r^3s^3}}$

Work Step by Step

Using the laws of exponents, the given expression, $ (2rs)^{-3/4} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{(2rs)^{3/4}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $ \dfrac{1}{(2rs)^{3/4}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{\sqrt[4]{(2rs)^{3}}} \\\\= \dfrac{1}{\sqrt[4]{2^3r^3s^3}} \\\\= \dfrac{1}{\sqrt[4]{8r^3s^3}} .\end{array}
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