Answer
$2xy$
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:
$\require{cancel}=\sqrt[3]{\dfrac{24x^3y^5}{3y^2}}
\\=\sqrt[3]{\dfrac{8\cancel{24}x^3\cancel{y^5}y^3}{\cancel{3y^2}}}
\\=\sqrt[3]{8x^3y^3}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\sqrt[3]{2^3x^3y^3}
\\=\sqrt[3]{(2xy)^3}$
Simplify to obtain:
$=2xy$
