# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set: 26

$\dfrac{3a}{b^2}\sqrt[5]{\dfrac{a^4}{b^3}}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[5]{\dfrac{243a^9}{b^{13}}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[5]{243a^9}}{\sqrt[5]{b^{13}}} \\\\= \dfrac{\sqrt[5]{243a^5\cdot a^4}}{\sqrt[5]{b^{10}\cdot b^3}} \\\\= \dfrac{\sqrt[5]{(3a)^5\cdot a^4}}{\sqrt[5]{(b^{2})^5\cdot b^3}} \\\\= \dfrac{3a\sqrt[5]{a^4}}{b^{2}\sqrt[5]{b^3}} \\\\= \dfrac{3a}{b^2}\sqrt[5]{\dfrac{a^4}{b^3}} \end{array} * Note that it is assumed that all variables represent positive numbers.

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