#### Answer

$\sqrt[7]{\dfrac{5x-15}{4x+8}}$

#### Work Step by Step

Using $\sqrt[a]{x}\sqrt[a]{y}=\sqrt[a]{xy}$, the given expression, $
\sqrt[7]{\dfrac{x-3}{4}}\sqrt[7]{\dfrac{5}{x+2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[7]{\dfrac{x-3}{4}\cdot\dfrac{5}{x+2}}
\\\\=
\sqrt[7]{\dfrac{5x-15}{4x+8}}
.\end{array}