#### Answer

$\sqrt[5]{(x-2)^3}$

#### Work Step by Step

Using $\sqrt[a]{x}\sqrt[a]{y}=\sqrt[a]{xy}$, the given expression, $
\sqrt[5]{x-2}\sqrt[5]{(x-2)^2}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt[5]{(x-2)(x-2)^2}
\\\\=
\sqrt[5]{(x-2)^3}
.\end{array}