Answer
$-12x^3y^4 \sqrt [4]{x^3}$.
Work Step by Step
The given expression is
$=(2x^2y\sqrt [4] {8xy})(-3xy^2\sqrt [4]{2x^2y^3})$
Clear the parentheses.
$=-6x^3y^3\sqrt [4] {8xy}\sqrt [4] {2x^2y^3}$
Apply the product rule of radicals.
$\sqrt [4]a \cdot \sqrt [4] b = \sqrt [4] {ab}$
$=-6x^3y^3\sqrt [4]{8xy\cdot 2x^2y^3}$
Find the square factors.
$=-6x^3y^3\sqrt [4]{2^4x^3y^4}$
Factor into two radicals.
$=-6x^3y^3\sqrt [4]{2^4y^4}\sqrt [4]{x^3}$
Simplify.
$=-6x^3y^3\cdot 2y \sqrt [4]{x^3}$
$=-12x^3y^4 \sqrt [4]{x^3}$.
