Answer
$\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}=2x^{2}\sqrt[4]{5y^{3}}$
Work Step by Step
$\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}$
Rewrite this expression as $\sqrt[4]{\dfrac{160x^{10}y^{5}}{2x^{2}y^{2}}}$ and evaluate the division inside the root:
$\dfrac{\sqrt[4]{160x^{10}y^{5}}}{\sqrt[4]{2x^{2}y^{2}}}=\sqrt[4]{\dfrac{160x^{10}y^{5}}{2x^{2}y^{2}}}=\sqrt[4]{80x^{10-2}y^{5-2}}=\sqrt[4]{80x^{8}y^{3}}=...$
Rewrite the expression inside the root as $16\cdot5\cdot x^{8}\cdot y^{3}$ and simplify:
$...=\sqrt[4]{16\cdot5\cdot x^{8}\cdot y^{3}}=2x^{2}\sqrt[4]{5y^{3}}$
