Answer
$\sqrt[12]{5+3x}$
Work Step by Step
Using the same indices for the radicals, the given expression, $
\dfrac{\sqrt[4]{(5+3x)^3}}{\sqrt[3]{(5+3x)^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[4(3)]{(5+3x)^{3(3)}}}{\sqrt[3(4)]{(5+3x)^{2(4)}}}
\\\\=
\dfrac{\sqrt[12]{(5+3x)^{9}}}{\sqrt[12]{(5+3x)^{8}}}
\\\\=
\sqrt[12]{\dfrac{(5+3x)^{9}}{(5+3x)^{8}}}
\\\\=
\sqrt[12]{(5+3x)^{9-8}}
\\\\=
\sqrt[12]{(5+3x)^{1}}
\\\\=
\sqrt[12]{5+3x}
\end{array}
* Note that it is assumed that all variables represent positive numbers.
