Answer
$\sqrt[]{a}$
Work Step by Step
Using $a^{m/n}=\sqrt[n]{a^m}$ and the laws of exponents, then,
\begin{array}{l}
\dfrac{\sqrt[3]{a^2}}{\sqrt[6]{a}}
\\\\=
\dfrac{a^{2/3}}{a^{1/6}}
\\\\=
a^{\frac{2}{3}-\frac{1}{6}}
\\\\=
a^{\frac{4}{6}-\frac{1}{6}}
\\\\=
a^{\frac{3}{6}}
\\\\=
a^{\frac{1}{2}}
\\\\=
\sqrt[]{a}
.\end{array}