The idea is that at first, we only have positive integral exponents.
To extend it to all integers, x^0 must be one if we want it to follow the index law. (in the case x ≠ 0)
x^0 * x^n = x^(0+n) = x^n , n is some positive integers.
x^0 = 1 (cancelling x^n in both sides)
The reason why we want it to follow the index law is that if so we can apply many known proporties of positive integral power exponentiation.
wait
do you mean 0^0 can be any number? i think it is not totally right. it should be no defined, i think. it is an intermediate form just like 0*infinity etc.
