Answer
$\frac{4x}{y^2}$.
Work Step by Step
The given expression is
$=\sqrt [3]{\frac{32x}{y^4}}\cdot \sqrt [3]{\frac{2x^2}{y^2}}$
Use the product rule.
$=\sqrt [3]{\frac{32x}{y^4}\cdot \frac{2x^2}{y^2}}$
Multiply
$=\sqrt [3]{\frac{64x^3}{y^6}}$
Factor the radicands as a perfect cube.
$=\sqrt [3]{\frac{4^3x^3}{(y^2)^3}}$
Simplify.
$=\frac{4x}{y^2}$.
