#### Answer

$\sqrt{ab}$

#### Work Step by Step

Using the laws of exponents and that $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(a^2b^2)^{1/4}
,$ is equivalent to
\begin{array}{l}\require{cancel}
((ab)^2)^{1/4}
\\\\=
(ab)^{2\cdot\frac{1}{4}}
\\\\=
(ab)^{2\cdot\frac{1}{4}}
\\\\=
(ab)^{\frac{2}{4}}
\\\\=
(ab)^{\frac{1}{2}}
\\\\=
\sqrt{(ab)^1}
\\\\=
\sqrt{ab}
.\end{array}