Chapter 5 - Section 5.2 - Negative Exponents and Scientific Notation - Exercise Set - Page 354: 49

$\frac{a^{30}}{b^{12}}$

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, $(a^{-5}b^{2})^{-6}=(a^{-5})^{-6}(b^{2})^{-6}=a^{-5\times-6}b^{2\times-6}=a^{30}b^{-12}=a^{30}\times\frac{1}{b^{12}}=\frac{a^{30}}{b^{12}}$.