Answer
$\frac{5\sqrt[3]{4 xy^2}}{2y}$
Work Step by Step
Given
\begin{equation}
\frac{5 x}{\sqrt[3]{2 x^2 y}}.
\end{equation} Simplify by rationalizing the denominator.
\begin{equation}
\begin{aligned} \frac{5 x}{\sqrt[3]{2 x^2 y}}&= \frac{5 x}{\sqrt[3]{2 x^2 y}}\cdot \frac{\sqrt[3]{2^2 x y^2}}{\sqrt[3]{2^2 x y^2}}\\
& =\frac{5 x \sqrt[3]{4 xy^2}}{\sqrt[3]{2^3 x^3 y^3}}\\
&= \frac{5x\sqrt[3]{4 xy^2}}{2xy}\\
&= \frac{5\sqrt[3]{4 xy^2}}{2y}.
\end{aligned}
\end{equation}
