Answer
$\sqrt[15]{(2x+1)^{4}}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[3]{(2x+1)^2}}{\sqrt[5]{(2x+1)^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[3(5)]{(2x+1)^{2(5)}}}{\sqrt[5(3)]{(2x+1)^{2(3)}}}
\\\\=
\dfrac{\sqrt[15]{(2x+1)^{10}}}{\sqrt[15]{(2x+1)^{6}}}
\\\\=
\sqrt[15]{\dfrac{(2x+1)^{10}}{(2x+1)^{6}}}
\\\\=
\sqrt[15]{(2x+1)^{10-6}}
\\\\=
\sqrt[15]{(2x+1)^{4}}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
