Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 34

$\dfrac{a^{12}}{b^{24}}$

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{a^{-3}}{b^{-6}} \right)^{-4} \\\\&= \dfrac{a^{-3(-4)}}{b^{-6(-4)}} \\\\&= \dfrac{a^{12}}{b^{24}} .\end{align*}