Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 224: 82

$\dfrac{1}{3x^3}$

Using the laws of exponents, the given expression, $ \left( \dfrac{3x^{-2}}{x^{-5}} \right)^{-1} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{3^{-1}x^{-2(-1)}}{x^{-5(-1)}} \\\\= \dfrac{3^{-1}x^{2}}{x^{5}} \\\\= 3^{-1}x^{2-5} \\\\= 3^{-1}x^{-3} \\\\= \dfrac{1}{3^{1}x^3} \\\\= \dfrac{1}{3x^3} .\end{array}