#### Answer

$\dfrac{1}{27}$

#### Work Step by Step

Using the laws of exponents, the given expression, $
\left( 27^{-2/3} \right)^{3/2}
,$ simplifies to
\begin{array}{l}\require{cancel}
27^{\left( -\frac{2}{3} \right) \left( \frac{3}{2} \right)}
\\\\=
27^{\left( -\frac{6}{6} \right)}
\\\\=
27^{-1}
\\\\=
\dfrac{1}{27^1}
\\\\=
\dfrac{1}{27}
.\end{array}