Answer
$a^3b^{3}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[]{(ab)^{6}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(ab)^{6/2}
\\\\=
(ab)^{3}
\\\\=
a^3b^{3}
.\end{array}
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