Answer
$5x\sqrt[3]{x^2y^2}$
Work Step by Step
RECALL:
$\dfrac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\dfrac{a}{b}}.$
Use the rule above to have
$\require{cancel}
\sqrt[3]{\dfrac{250x^7y^3}{2x^2y}}
\\=\sqrt[3]{\dfrac{\cancel{250}125\cancel{x^7}x^5\cancel{y^3}y^2}{\cancel{2x^2y}}}
\\=\sqrt[3]{125x^5y^2}
\\=\sqrt[3]{125x^3(x^2y^2)}
\\=\sqrt[3]{(5x)^3(x^2y^2)}
\\=5x\sqrt[3]{x^2y^2}.$
