If xy does not equal zero, what is the value of xy?

[TylerC115]

If xy does not equal zero, what is the value of xy?

(1) 2/x + 2/y = 3
(2) x^3 - (2/y)^3 = 0

I understand that B is correct. I had a question on the logic behind it - I've run into problems before in assuming that a cube root is positive, while not accounting for the possibility it is negative. My question is - what exactly is the rule when it comes to "assuming" the sign of variables raised to a power?

[Sage Pearce-Higgins]

The rule is a simple one: even powers are always positive (or zero), while odd powers keep the sign of the number you started with - they can be either positive or negative.

However, that sounds a bit abstract and is probably hard to remember. What I suggest is that you do some "playful studying". Take a few numbers, such as 1, 2, 3 and -1, -2, -3, and raise them to a few different powers. After you've done this, try raising them to some negative powers. You could even try out some fractions for a further step.