Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set - Page 353: 37

$\frac{1}{a^{2}}$

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, $\frac{(a^{5})^{2}}{(a^{3})^{4}}=\frac{a^{5\times2}}{a^{3\times4}}=\frac{a^{10}}{a^{12}}=a^{10-12}=a^{-2}=\frac{1}{a^{2}}$.