Data Sufficiency (DS) | Re: If ab 0, does a=b?

\(x^{a-b}=1\) does not necessarily mean that a - b = 0.

If x = 1, then a - b can be any number:\(1^{a-b}=1\) is true for all values of a - b.
If x = -1, then a - b can be any EVEN number:\((-1)^{a-b}=1\) is true for all EVEN values of a -b.
Above, one of the posts says that x can be 0 there but 0^0 case is not tested on the GMAT because there is no consensus, as far as I know, about this case. Some say 0^0 = 1, some say 0^0 is notdefined.

So, if we knew that x is not 1, -1, or 0, then we could deduce that a - b = 0 but we don't know that for (1), so the first statement is notsufficient.