Chapter 5 - Section 5.2 - More Work with Exponents and Scientific Notation - Exercise Set - Page 268: 66

$9y^{12a-2}$

Using laws of exponents, the given expression simplifies to \begin{align*} & \left( \dfrac{3y^{5a}}{y^{-a+1}} \right)^2 \\\\&= \dfrac{3^2y^{2(5a)}}{y^{2(-a+1)}} \\\\&= \dfrac{9y^{10a}}{y^{-2a+2}} \\\\&= 9y^{10a-(-2a+2)} \\\\&= 9y^{10a+2a-2} \\\\&= 9y^{12a-2} .\end{align*}