Chapter 10 - Exponents and Radicals - 10.2 Rational Numbers as Exponents - 10.2 Exercise Set - Page 641: 80

$\dfrac{1}{27}$

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}