Answer
$-2xy\sqrt { 2y}$.
Work Step by Step
The given expression is
$=5\sqrt {8x^2y^3}-\frac{9x^2\sqrt {64y}}{3x\sqrt {2y^{-2}}}$
Divide the radicands and retain the common index.
$=5\sqrt {2^3x^2y^3}-\frac{3^2x^2}{3x}\cdot\sqrt {\frac{2^6y}{2y^{-2}}}$
Divide factors. Subtract exponents on common bases.
$=5\sqrt {2^3x^2y^3}-3^{2-1}x^{2-1}\cdot\sqrt {2^{6-1}y^{1+2}}$
Simplify.
$=5\sqrt {2^3x^2y^3}-3^{1}x^{1}\cdot\sqrt {2^{5}y^{3}}$
$=5\cdot 2xy\sqrt {2y}-3x\cdot2^2y\sqrt {2y}$
Simplify.
$=10xy\sqrt {2y}-12xy\sqrt {2y}$
Apply the distributive property.
$=(10xy-12xy)\sqrt { 2y}$
Simplify.
$=-2xy\sqrt { 2y}$.
