Chapter 4 - Polynomials - Mid-Chapter Review - Mixed Review - Page 263: 8

$\dfrac{a^{2}}{bc^{3}}$

Using the laws of exponents, the given expression, $ (a^{-2}bc^3)^{-1} $, is equivalent to \begin{array}{l}\require{cancel} a^{-2(-1)}b^{-1}c^{3(-1)} \\\\= a^{2}b^{-1}c^{-3} \\\\= \dfrac{a^{2}}{b^{1}c^{3}} \\\\= \dfrac{a^{2}}{bc^{3}} .\end{array}