Chapter 7 - Exponents and Exponential Functions - 7-4 More Multiplication Properties of Exponents - Practice and Problem-Solving Exercises - Page 437: 51

$(y^{-4})^{-3}=y^{12}$

$(y^{-4})^{?}=y^{12}$ To raise a power to a power, we multiply the exponents. Therefore, in order for this equation to be correct, the product of $-4$ and the second exponent must equal $12$. The only way this would work is if the second exponent is $-3$, because $-4\times-3=12$. Therefore the correct equation is $(y^{-4})^{-3}=y^{12}$