# Chapter 10 - Exponents and Radicals - 10.4 Dividing Radical Expressions - 10.4 Exercise Set - Page 653: 24

$\dfrac{x^2y^{3}}{z}\sqrt[4]{\dfrac{x}{z^2}}$

#### Work Step by Step

Using the properties of radicals, the given expression, $\sqrt[4]{\dfrac{x^9y^{12}}{z^{6}}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[4]{x^9y^{12}}}{\sqrt[4]{z^{6}}} \\\\= \dfrac{\sqrt[4]{x^8y^{12}\cdot x}}{\sqrt[4]{z^{4}\cdot z^2}} \\\\= \dfrac{\sqrt[4]{(x^2y^{3})^4\cdot x}}{\sqrt[4]{(z)^{4}\cdot z^2}} \\\\= \dfrac{x^2y^{3}\sqrt[4]{x}}{z\sqrt[4]{z^2}} \\\\= \dfrac{x^2y^{3}}{z}\sqrt[4]{\dfrac{x}{z^2}} \end{array} * Note that it is assumed that all variables represent positive numbers.

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