Answer
$\dfrac{1}{9}$
Work Step by Step
Using $a^{-x}=\dfrac{1}{a^x}$ and $a^{m/n}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$, the given expression, $
(-27)^{-2/3}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{1}{(-27)^{2/3}}
\\\\=
\dfrac{1}{(\sqrt[3]{-27})^{2}}
\\\\=
\dfrac{1}{\left( \sqrt[3]{(-3)^3} \right)^{2}}
\\\\=
\dfrac{1}{(-3)^{2}}
\\\\=
\dfrac{1}{9}
.\end{array}
