Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 40

$\dfrac{16}{n^{20}m^{8}}$

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{n^{5}}{2m^{-2}} \right)^{-4} \\\\&= \dfrac{n^{5(-4)}}{2^{-4}m^{-2(-4)}} \\\\&= \dfrac{n^{-20}}{2^{-4}m^{8}} \\\\&= \dfrac{2^4}{n^{20}m^{8}} \\\\&= \dfrac{16}{n^{20}m^{8}} .\end{align*}