Answer
$y\sqrt[3]{6}$
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[3]{60xy^3}}{\sqrt[3]{10x}}
\\\\=
\sqrt[3]{\dfrac{60xy^3}{10x}}
\\\\=
\sqrt[3]{\dfrac{\cancel{10}(6)\cancel{x}y^3}{\cancel{10}\cancel{x}}}
\\\\=
\sqrt[3]{6y^3}
.\end{array}
Extracting the factors that are perfect powers of the index, the expression above simplifies to
\begin{array}{l}\require{cancel}
\sqrt[3]{6y^3}
\\\\=
\sqrt[3]{y^3\cdot 6}
\\\\=
\sqrt[3]{(y)^3\cdot 6}
\\\\=
y\sqrt[3]{6}
.\end{array}
