Answer
$\dfrac{\sqrt[3]{2xy^2}}{xy}$
Work Step by Step
Multiplying the given expression, $
\sqrt[3]{\dfrac{2}{x^2y}}
,$ by an expression equal to $1$ such that the denominator becomes a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{2}{x^2y}}
\\\\=
\sqrt[3]{\dfrac{2}{x^2y}\cdot\dfrac{xy^2}{xy^2}}
\\\\=
\sqrt[3]{\dfrac{2xy^2}{x^3y^3}}
.\end{array}
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{\dfrac{2xy^2}{x^3y^3}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{x^3y^3}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{(xy)^3}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{xy}
.\end{array}
