Chapter 5 - Section 5.7 - Negative Exponents and Scientific Notation - Exercise Set - Page 408: 42

$-\dfrac{1}{3a^5}$

Using the laws of exponents, the given expression, $ \dfrac{-15a^8}{45a^{13}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{-\cancel{15}a^{8-13}}{\cancel{15}(3)} \\\\= \dfrac{-(a)^{-5}}{3} \\\\= \dfrac{-1}{3a^5} \\\\= -\dfrac{1}{3a^5} .\end{array}