Answer
$\sqrt[12]{x^{2}y^{5}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[4]{x^2y^3}}{\sqrt[3]{xy}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[4(3)]{x^{2(3)}y^{3(3)}}}{\sqrt[3(4)]{x^{1(4)}y^{1(4)}}}
\\\\=
\dfrac{\sqrt[12]{x^{6}y^{9}}}{\sqrt[12]{x^{4}y^{4}}}
\\\\=
\sqrt[12]{\dfrac{x^{6}y^{9}}{x^{4}y^{4}}}
\\\\=
\sqrt[12]{x^{6-4}y^{9-4}}
\\\\=
\sqrt[12]{x^{2}y^{5}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
