Answer
$-2xy\sqrt[5]{xy^2}
$
Work Step by Step
Extracting the perfect powers of the index, the given expression, $
\sqrt[5]{-32x^6y^7}
,$ is equivalent to
\begin{align*}
&
=\sqrt[5]{-32x^5y^5\cdot xy^2}
\\\\&=
\sqrt[5]{(-2xy)^5\cdot xy^2}
\\\\&=
-2xy\sqrt[5]{xy^2}
.\end{align*}
Hence, the simplified form of the given expression is $
-2xy\sqrt[5]{xy^2}
$.
