Answer
$\frac{5\sqrt[5] {8x^2y^4}} {x}$.
Work Step by Step
The given expression is
$=\frac{10y}{\sqrt[5] {4x^3y}}\cdot\frac{\sqrt[5] {8x^2y^4}}{\sqrt[5] {8x^2y^4}}$
Multiply the radicands and retain the common index.
$=10y\cdot\frac{\sqrt[5] {8x^2y^4}}{\sqrt[5] {8x^2y^4\cdot 4x^3y}}$
Multiply the factors. Add exponents of common bases.
$=10y\cdot\frac{\sqrt[5] {8x^2y^4}}{\sqrt[5] {32x^{2+3}y^{4+1}}}$
Simplify.
$=10y\cdot\frac{\sqrt[5] {8x^2y^4}}{\sqrt[5] {32x^5y^5}}$
Divide the radicands and retain the common index.
$=10y\cdot\sqrt[5] {\frac{8x^2y^4} {32x^5y^5}}$
Rewrite $32$ as $2^5$.
$=10y\cdot\sqrt[5] {\frac{8x^2y^4} {2^5x^5y^5}}$
Simplify.
$=\frac{10y\cdot \sqrt[5] {8x^2y^4}} {2xy}$
$=\frac{5y\cdot \sqrt[5] {8x^2y^4}} {x}$.
