Answer
$14xy^2\sqrt[3]{x}$
Work Step by Step
Using the properties of radicals, the expression $
\dfrac{7\sqrt[3]{48x^4y^8}}{\sqrt[3]{6y^2}}
$ simplifies to
\begin{array}{l}
7\sqrt[3]{\dfrac{48x^4y^8}{6y^2}}
\\\\=
7\sqrt[3]{8x^4y^{8-2}}
\\\\=
7\sqrt[3]{8x^4y^{6}}
\\\\=
7\sqrt[3]{8x^3y^{6}\cdot x}
\\\\=
7\cdot2xy^2\sqrt[3]{x}
\\\\=
14xy^2\sqrt[3]{x}
.\end{array}
