Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set - Page 353: 42

$-\frac{1}{a}$

We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $\frac{15a^{4}}{-15a^{5}}=\frac{15}{-15}\times a^{4-5}=-1\times a^{-1}=-1\times\frac{1}{a}=-\frac{1}{a}$.