Answer
$-8x^4y^{10}\sqrt[5] {xy^2}$.
Work Step by Step
The given expression is
$=-4x^2y^7(\sqrt[5] {-32x^{11}y^{17}})$
$=-4x^2y^7\sqrt[5] {(-1)^5\cdot 2^5\cdot x^{10}\cdot x^1 \cdot y^{15}\cdot y^2}$
Group the perfect fifth factors.
$=-4x^2y^7\sqrt[5] { \left [(-1)^5 2^5 x^{10}y^{15} \right ] \left[ x^1 y^2 \right ]}$
Factor into two radicals.
$=-4x^2y^7\sqrt[5] {(-1)^5 2^5 x^{10}y^{15}}\cdot \sqrt[5] {x^1y^2}$
Simplify.
$=-4x^2y^7\cdot (-1)2x^2y^3\sqrt[5] {xy^2}$
$=-8x^4y^{10}\sqrt[5] {xy^2}$.
