# Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 100

$x^{8}y^{20}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $\left( \sqrt[3]{x^2y^5} \right)^{12} ,$ is equivalent to \begin{array}{l}\require{cancel} (x^2y^5)^{12/3} \\\\= (x^2y^5)^{4} \\\\= x^{2(4)}y^{5(4)} \\\\= x^{8}y^{20} .\end{array}

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