Answer
$\sqrt[15]{x^{7}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[3]{x^2}}{\sqrt[5]{x}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3(5)]{x^{2(5)}}}{\sqrt[5(3)]{x^{1(3)}}}
\\\\=
\dfrac{\sqrt[15]{x^{10}}}{\sqrt[15]{x^{3}}}
\\\\=
\sqrt[15]{\dfrac{x^{10}}{x^{3}}}
\\\\=
\sqrt[15]{x^{10-3}}
\\\\=
\sqrt[15]{x^{7}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
