Answer
$\sqrt[10]{y-9}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[5]{(y-9)^3}}{\sqrt[]{y-9}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[5(2)]{(y-9)^{3(2)}}}{\sqrt[2(5)]{(y-9)^{1(5)}}}
\\\\=
\dfrac{\sqrt[10]{(y-9)^{6}}}{\sqrt[10]{(y-9)^{5}}}
\\\\=
\sqrt[10]{\dfrac{(y-9)^{6}}{(y-9)^{5}}}
\\\\=
\sqrt[10]{(y-9)^{6-5}}
\\\\=
\sqrt[10]{(y-9)^{1}}
\\\\=
\sqrt[10]{y-9}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
