Answer
$-2ab^{2}\sqrt[5]{a^2b}$
Work Step by Step
Extracting the factors that are perfect roots of the given index, the given expression, $
\sqrt[5]{-32a^7b^{11}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{-32a^5b^{10}\cdot a^2b}
\\\\=
\sqrt[5]{(-2ab^{2})^5\cdot a^2b}
\\\\=
-2ab^{2}\sqrt[5]{a^2b}
\end{array}
* Note that it is assumed that no radicands were formed by raising negative numbers to even powers.