Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 23

$4a^{8}b^{4}$

Using laws of exponents, the given expression simpifies to \begin{align*} & \left( \dfrac{2a^{-2}b^5}{4a^2b^7} \right)^{-2} \\\\&= \left( \dfrac{a^{-2-2}b^{5-7}}{2} \right)^{-2} \\\\&= \left( \dfrac{a^{-4}b^{-2}}{2} \right)^{-2} \\\\&= \dfrac{a^{-4(-2)}b^{-2(-2)}}{2^{-2}} \\\\&= 2^2a^{8}b^{4} \\&= 4a^{8}b^{4} .\end{align*}