What would (y^-2)^2 be?

(y^-2)² = (y^-2 * y^-2), which is:
y^-4.

y^(- 4) = 1 / y^4

y^-4
multiply the exponents

If there is a indice inside brackets, and one outside brackets, to multiply the numbers, you multiply the indices.
-2 x 2 = -4
So the answer is y^-4

(y^-2)^2
= (y^-2)(y^-2)
= (1/y^2)(1/y^2)
= 1/y^4 (y^-4)

it is y^-4 because y^(-2*2) = y^-4

(y^-2)^2 = y^(-2*2) = y^(-4).

-John