Answer
$\dfrac{\sqrt[3]{2xy^2}}{2y}$
Work Step by Step
Multiplying by an expression equal to $1$ which will make the denominator a perfect power of the index, the given expression is equivalent to\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3]{x}}{\sqrt[3]{4y}}
\\\\=
\dfrac{\sqrt[3]{x}}{\sqrt[3]{4y}}\cdot\dfrac{\sqrt[3]{2y^2}}{\sqrt[3]{2y^2}}
\\\\=
\dfrac{\sqrt[3]{x(2y^2)}}{\sqrt[3]{4y(2y^2)}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{8y^3}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{\sqrt[3]{(2y)^3}}
\\\\=
\dfrac{\sqrt[3]{2xy^2}}{2y}
.\end{array}
