#### Answer

$2x^{2}y^{3}\sqrt[4]{y^3}$

#### Work Step by Step

Using the properties of radicals, the given expression, $
\dfrac{\sqrt[4]{48x^9y^{13}}}{\sqrt[4]{3xy^{-2}}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[4]{\dfrac{48x^9y^{13}}{3xy^{-2}}}
\\\\=
\sqrt[4]{16x^{9-1}y^{13-(-2)}}
\\\\=
\sqrt[4]{16x^{8}y^{15}}
\\\\=
\sqrt[4]{16x^{8}y^{12}\cdot y^3}
\\\\=
\sqrt[4]{(2x^{2}y^{3})^4\cdot y^3}
\\\\=
2x^{2}y^{3}\sqrt[4]{y^3}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.