Chapter 4 - Section 4.1 - Integer Exponents and Scientific Notation - 4.1 Exercises - Page 278: 139

$\dfrac{y^{9}}{8}$

Using the laws of exponents, the given expression, $ \dfrac{2^2y^4(y^{-3})^{-1}}{2^5y^{-2}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{2^2y^4(y^{-3(-1)})}{2^5y^{-2}} \\\\= \dfrac{2^2y^4y^{3}}{2^5y^{-2}} \\\\= 2^{2-5}y^{4+3-(-2)} \\\\= 2^{-3}y^{4+3+2} \\\\= \dfrac{y^{9}}{2^3} \\\\= \dfrac{y^{9}}{8} .\end{array}