Answer
$\sqrt[10]{xy^{3}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[5]{x^3y^4}}{\sqrt[]{xy}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[5(2)]{x^{3(2)}y^{4(2)}}}{\sqrt[2(5)]{x^{1(5)}y^{1(5)}}}
\\\\=
\dfrac{\sqrt[10]{x^{6}y^{8}}}{\sqrt[10]{x^{5}y^{5}}}
\\\\=
\sqrt[10]{\dfrac{x^{6}y^{8}}{x^{5}y^{5}}}
\\\\=
\sqrt[10]{x^{6-5}y^{8-5}}
\\\\=
\sqrt[10]{x^{1}y^{3}}
\\\\=
\sqrt[10]{xy^{3}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
