Answer
$\sqrt[6]{(7-y)^{5}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[]{(7-y)^3}}{\sqrt[3]{(7-y)^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[2(3)]{(7-y)^{3(3)}}}{\sqrt[3(2)]{(7-y)^{2(2)}}}
\\\\=
\dfrac{\sqrt[6]{(7-y)^{9}}}{\sqrt[6]{(7-y)^{4}}}
\\\\=
\sqrt[6]{\dfrac{(7-y)^{9}}{(7-y)^{4}}}
\\\\=
\sqrt[6]{(7-y)^{9-4}}
\\\\=
\sqrt[6]{(7-y)^{5}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
