#### Answer

$27y^{9}$

#### Work Step by Step

Using $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(9y^6)^{3/2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[]{(9y^6)^{3}}
\\\\=
\left( \sqrt[]{9y^6} \right)^3
\\\\=
\left( \sqrt[]{(3y^3)^2} \right)^3
\\\\=
\left( 3y^3 \right)^3
\\\\=
3^3y^{3(3)}
\\\\=
27y^{9}
.\end{array}