#### Answer

$\sqrt[15]{\dfrac{a^{7}}{b^{2}}}$

#### Work Step by Step

Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[5]{a^4b}}{\sqrt[3]{ab}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[5(3)]{a^{4(3)}b^{1(3)}}}{\sqrt[3(5)]{a^{1(5)}b^{1(5)}}}
\\\\=
\dfrac{\sqrt[15]{a^{12}b^{3}}}{\sqrt[15]{a^{5}b^{5}}}
\\\\=
\sqrt[15]{\dfrac{a^{12}b^{3}}{a^{5}b^{5}}}
\\\\=
\sqrt[15]{a^{12-5}b^{3-5}}
\\\\=
\sqrt[15]{a^{7}b^{-2}}
\\\\=
\sqrt[15]{\dfrac{a^{7}}{b^{2}}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.