Chapter 5 - Exponents and Polynomials - 5.6 - Integral Exponents and Scientific Notation - Problem Set 5.6 - Page 224: 75

$a^{4}b^{8}$

Using the laws of exponents, the given expression, $ \left( \dfrac{a^{-1}}{b^{2}} \right)^{-4} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{a^{-1(-4)}}{b^{2(-4)}} \\\\= \dfrac{a^{4}}{b^{-8}} \\\\= a^{4}b^{8} .\end{array}