#### Answer

$\sqrt[4]{a}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
\sqrt[12]{a^3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
a^{3/12}
\\\\=
a^{1/4}
\\\\=
\sqrt[4]{a^1}
\\\\=
\sqrt[4]{a}
.\end{array}