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

Published by Pearson

# Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 56

#### Answer

$\dfrac{1}{\sqrt[6]{3,125x^5y^{5}}}$

#### Work Step by Step

Using the laws of exponents, the given expression, $(5xy)^{-5/6} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{1}{(5xy)^{5/6}} .\end{array} Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the expression, $\dfrac{1}{(5xy)^{5/6}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{1}{\sqrt[6]{(5xy)^{5}}} \\\\= \dfrac{1}{\sqrt[6]{5^5x^5y^{5}}} \\\\= \dfrac{1}{\sqrt[6]{3,125x^5y^{5}}} .\end{array}

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