Are buying a drink and buying popcorn independent or dependant events

I see.

The correct way to write these is

A: 3^-2 * 3^ - 2 = 1/9 * 1/9 = 1/81 and this one is fine.

B: 3^-4 = (1/3)^ 4 = 1/3 * 1/3 * 1/3 * 1/3 = 1/81 and this one works.

C: (3^-2)^2 = (1/9)^2 = 1/81 and this one also works.

D: No matter how you interpret this, it is not going to equal 1/81. I think it might be written as -(3)^2 * - (3)^2 = - 9 * - 9 = 81 which is not correct.

D