Answer
$3mn^2\sqrt[3]{4m^2p}$
Work Step by Step
Given \begin{equation}
\sqrt[3]{108 m^5 n^6 p}.
\end{equation} Simplify by factoring out perfect cubes.
\begin{equation}
\begin{aligned}
\sqrt[3]{108 m^5 n^6 p}&=\sqrt[3]{4\cdot3^3\cdot m^3\cdot m^2\cdot (n^2)^3\cdot p} \\
&=3mn^2\sqrt[3]{4m^2p}.
\end{aligned}
\end{equation}
