Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 223: 17

$\dfrac{27}{64}$

Using $a^{-x}=\dfrac{1}{a^x}$ or $\dfrac{1}{a^{-x}}=a^x$ and the laws of exponents, the given expression, $ \dfrac{1}{\left( \dfrac{3}{4} \right)^{-3}} ,$ is equivalent to \begin{array}{l}\require{cancel} \left( \dfrac{3}{4} \right)^{3} \\\\= \dfrac{3^3}{4^3} \\\\= \dfrac{27}{64} .\end{array}