Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 223: 30

$\dfrac{1}{216}$

Using the laws of exponents, the given expression, $ \left( \dfrac{3^{}}{2^{-1}} \right)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{3^{1(-3)}}{2^{-1(-3)}} \\\\= \dfrac{3^{-3}}{2^{3}} \\\\= \dfrac{1}{3^{3}\cdot2^{3}} \\\\= \dfrac{1}{27\cdot8} \\\\= \dfrac{1}{216} .\end{array}