Answer
$\dfrac{xy}{\sqrt[3]{10x^2yz}}$
Work Step by Step
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}
