Answer
$x^3y^{10}z^2 \sqrt[3] {4xz} $.
Work Step by Step
The given expression is
$=\frac{-x^2y^7}{2}\left ( \sqrt[3] {-32x^4y^9z^7} \right )$
Identify perfect cube factors.
$=\frac{-x^2y^7}{2}\left ( \sqrt[3] {(-1)^32^32^2x^3x^1y^3y^3y^3z^3z^3z^1} \right )$
Factor into two radicals.
$=\frac{-x^2y^7}{2}\left ( \sqrt[3] {(-1)^32^3x^3y^3y^3y^3z^3z^3}\sqrt[3] {2^2x^1z^1} \right )$
$=\frac{-x^2y^7}{2}\cdot (-1)2xyyyzz\left ( \sqrt[3] {4xz} \right )$
Simplify.
$=x^3y^{10}z^2\left ( \sqrt[3] {4xz} \right )$.
