Answer
$10x^2\sqrt{xy}$.
Work Step by Step
$=\frac{\sqrt{200x^3y^2}}{\sqrt{2x^{-2}y}}$
Use quotient rule.
$=\sqrt{\frac{200x^3y^2}{2x^{-2}y}}$
Simplify.
$=\sqrt{100x^{3+2}y^{2-1}}$
$=\sqrt{100x^{5}y^{1}}$
Factor as a perfect square.
$=\sqrt{10^2x^{4}xy}$
Use product rule.
$=\sqrt{10^2x^{4}}\sqrt{xy}$
Simplify.
$=10x^2\sqrt{xy}$.
