Answer
$2xy\sqrt[3] {2y^2}$.
Work Step by Step
The given expression is
$=\sqrt[3] {4x^2y}\cdot \sqrt[3] {4xy^4}$
Use the product rule.
$=\sqrt[3] {4x^2y\cdot 4xy^4}$
Simplify.
$=\sqrt[3] {16x^3y^5}$
Factor the terms as a perfect cube.
$=\sqrt[3] {2^3\cdot 2x^3y^3y^2}$
Group the perfect cubes.
$=\sqrt[3] {(2^3x^3y^3)(2y^2)}$
Use the product rule
$=\sqrt[3] {2^3x^3y^3}\sqrt[3] {2y^2}$
Simplify.
$=2xy\sqrt[3] {2y^2}$.
