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.
The case x = 0 is much more complicated
you may see:
http://en.wikipedia.org/wiki/0%5E0#Zero_to_the_zero_power
