Answer
$7x\sqrt { 3xy}$.
Work Step by Step
The given expression is
$=2x\sqrt {75xy}-\frac{\sqrt {81xy^2}}{\sqrt {3x^{-2}y}}$
Divide the radicands and retain the common index.
$=2x\sqrt {5^2\cdot 3xy}-\sqrt {\frac{3^4xy^2}{ {3x^{-2}y}}}$
Divide factors in the radicand. Subtract exponents on common bases.
$=2x\sqrt {5^2\cdot 3xy}-\sqrt {3^{4-1}x^{1+2}y^{2-1}}$
Simplify.
$=2x\sqrt {5^2\cdot 3xy}-\sqrt {3^3x^{3}y^{1}}$
$=2x\cdot 5\sqrt { 3xy}-3x\sqrt {3xy}$
Simplify.
$=10x\sqrt { 3xy}-3x\sqrt {3xy}$
By using the distributive property:
$=(10x-3x)\sqrt { 3xy}$
Simplify.
$=7x\sqrt { 3xy}$.
