Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises - Page 278: 117

$\dfrac{625}{a^{10}}$

Using the laws of exponents, the given expression, $ (5a^{-1})^4(a^2)^{-3} ,$ is equivalent to \begin{array}{l}\require{cancel} 5^4a^{-1(4)}(a^{2(-3)}) \\\\= 5^4a^{-4}(a^{-6}) \\\\= 5^4a^{-4+(-6)} \\\\= 5^4a^{-4-6} \\\\= 5^4a^{-10} \\\\= \dfrac{5^4}{a^{10}} \\\\= \dfrac{625}{a^{10}} .\end{array}