Answer
$-6x^3y^3\sqrt {2}$.
Work Step by Step
The given expression is
$=(-2xy^2\sqrt {3x})(xy\sqrt {6x})$
Clear the parentheses.
$=-2x^2y^3\sqrt {3x}\sqrt {6x}$
Apply the product rule of radicals.
$\sqrt a \cdot \sqrt b = \sqrt {ab}$
$=-2x^2y^3\sqrt {3x\cdot 6x}$
Find the square factors.
$=-2x^2y^3\sqrt {3^2x^22}$
Factor into two radicals.
$=-2x^2y^3\sqrt {3^2x^2}\sqrt {2}$
Simplify.
$=-2x^2y^3\cdot 3x\sqrt {2}$
$=-6x^3y^3\sqrt {2}$.
