Answer
$3x\sqrt [3] {5xy}$.
Work Step by Step
The given expression is
$=\frac{15x^4\sqrt [3] {80x^3y^2}}{5x^3\sqrt [3]{2x^2y}}-\frac{75\sqrt [3]{5x^3y}}{25\sqrt[3] {x^{-1}}}$
Divide the radicands and retain the common index.
$=\frac{15x^4}{5x^3}\cdot\sqrt [3] {\frac{80x^3y^2}{2x^2y}}-\frac{75}{25}\sqrt [3]{\frac{5x^3y}{x^{-1}}}$
Divide factors. Subtract exponents on common bases.
$=3x^{4-3}\cdot\sqrt [3] {40x^{3-2}y^{2-1}}-3\sqrt [3]{5x^{3+1}y}$
Simplify.
$=3x^{1}\cdot\sqrt [3] {40x^{1}y^{1}}-3\sqrt [3]{5x^{4}y}$
$=3x\cdot2\sqrt [3] {5xy}-3x\sqrt [3]{5xy}$
Simplify.
$=6x\sqrt [3] {5xy}-3x\sqrt [3]{5xy}$
Apply the distributive property.
$=(6x-3x)\sqrt [3] {5xy}$
Simplify.
$=3x\sqrt [3] {5xy}$.
