#### Answer

$-2a^2\sqrt[3]{4}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\sqrt[3]{-32a^6}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{-8a^6\cdot4}
\\\\=
\sqrt[3]{(-2a^2)^3\cdot4}
\\\\=
-2a^2\sqrt[3]{4}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.