Answer
$ \frac{5\sqrt[3]{9m^2n}}{3n}$
Work Step by Step
Given \begin{equation}
\frac{5 m}{\sqrt[3]{3 m n^2}}.
\end{equation} Rationalize the denominator and simplify.
\begin{equation}
\begin{aligned}
\frac{5 m}{\sqrt[3]{3 m n^2}}&=\frac{5 m}{\sqrt[3]{3 m n^2}}\cdot \frac{\sqrt[3]{3^2m^2n}}{\sqrt[3]{3^2m^2n}}\\
&= \frac{5m\sqrt[3]{3^2m^2n}}{\sqrt[3]{3^3m^3n^3}}\\
& = \frac{5m\sqrt[3]{3^2m^2n}}{3mn}\\
&= \frac{5\sqrt[3]{9m^2n}}{3n}.
\end{aligned}
\end{equation} The simplified expression is \begin{equation}
\frac{5 m}{\sqrt[3]{3 m n^2}}= \frac{5\sqrt[3]{9m^2n}}{3n}.
\end{equation}
