# Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 55

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

#### 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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