Answer
$\sqrt[12]{a^{5}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[3]{a^2}}{\sqrt[4]{a}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3(4)]{a^{2(4)}}}{\sqrt[4(3)]{a^{1(3)}}}
\\\\=
\dfrac{\sqrt[12]{a^{8}}}{\sqrt[12]{a^{3}}}
\\\\=
\sqrt[12]{\dfrac{a^{8}}{a^{3}}}
\\\\=
\sqrt[12]{a^{8-3}}
\\\\=
\sqrt[12]{a^{5}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
