Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 45

$\dfrac{1}{y^{15}}$

Using laws of exponents, the given expression simplifies to \begin{align*} & \dfrac{(y^3)^{-4}}{y^3} \\\\&= \dfrac{y^{3(-4)}}{y^3} \\\\&= \dfrac{y^{-12}}{y^3} \\\\&= y^{-12-3} \\&= y^{-15} \\\\&= \dfrac{1}{y^{15}} .\end{align*}