Intermediate Algebra (6th Edition)

$\dfrac{xy}{\sqrt[3]{10x^2yz}}$
Multiplying both the numerator and the denominator by a factor that will make the numerator a perfect power of the radical, the rationalized-numerator form of the given expression, $\sqrt[3]{\dfrac{xy^2}{10z}} ,$ is \begin{array}{l}\require{cancel} \sqrt[3]{\dfrac{xy^2}{10z}\cdot\dfrac{x^2y}{x^2y}} \\\\= \sqrt[3]{\dfrac{x^3y^3}{10x^2yz}} \\\\= \sqrt[3]{\dfrac{(xy)^3}{10x^2yz}} \\\\= \dfrac{xy}{\sqrt[3]{10x^2yz}} .\end{array}