Answer
$5y\sqrt[3]{x^2}$
Work Step by Step
RECALL:
(1) The quotient rule:
$\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
(2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne =0$
Use the quotient rule above to obtain:
$\require{cancel}=\sqrt[3]{\dfrac{250x^5y^3}{2x^3}}
\\=\sqrt[3]{\dfrac{125\cancel{250}\cancel{x^5}x^2y^3}{\cancel{2x^3}}}
\\=\sqrt[3]{125x^2y^3}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\sqrt[3]{125y^3(x^2)}
\\=\sqrt[3]{5^3y^3(x^2)}
\\=\sqrt[3]{(5y)^3(x^2)}$
Simplify to obtain:
$=5y\sqrt[3]{x^2}$
