Answer
$2ab^2c^2\sqrt[3]{4ab^2}$
Work Step by Step
Given \begin{equation}
\sqrt[3]{32 a^4 b^8 c^6}.
\end{equation} Write the radicand as a power of $3$ and take the cube root.
\begin{equation}
\begin{aligned}
\sqrt[3]{32 a^4 b^8 c^6}&=\sqrt[3]{2^3\cdot 2^2 a^3\cdot a (b^2)^3b^2 (c^2)^3}\\
&= 2ab^2c^2\sqrt[3]{4ab^2}.
\end{aligned}
\end{equation} We got: \begin{equation}
\sqrt[3]{32 a^4 b^8 c^6}= 2ab^2c^2\sqrt[3]{4ab^2}.
\end{equation}
