#### Answer

$\sqrt[5]{3x^{4}y}$

#### Work Step by Step

Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[5]{48x^6y^{10}}}{\sqrt[5]{16x^2y^9}}
\\\\=
\sqrt[5]{\dfrac{48x^6y^{10}}{16x^2y^9}}
\\\\=
\sqrt[5]{\dfrac{\cancel{16}(3)x^{6-2}y^{10-9}}{\cancel{16}}}
\\\\=
\sqrt[5]{3x^{4}y^{1}}
\\\\=
\sqrt[5]{3x^{4}y}
.\end{array}