Answer
$-5x^2y\sqrt[3]{2y^2}$
Work Step by Step
Extracting the perfect powers of the index, the given expression, $
\sqrt[3]{-250x^6y^5}
,$ is equivalent to
\begin{align*}
&
\sqrt[3]{-125x^6y^3\cdot2y^2}
\\\\&=
\sqrt[3]{\left(-5x^2y\right)^3\cdot2y^2}
\\\\&=
-5x^2y\sqrt[3]{2y^2}
.\end{align*}
Hence, the simplified form of the given expression is $
-5x^2y\sqrt[3]{2y^2}
$.