Although standard mathematica notation glosses over the difference, it's important to distinguish between the following two versions of the power operation, which I'll call pow1 and pow2:
pow1(x, y) = x^y where y is any integer
pow2(x, y) = x^y where y is any real
The value of 0^0 is 1 for (pow-a) and 0 for (pow-b).
The value of 0^0 is 1 for (pow-a) and 0 for (pow-b).