> Defining 0^0 = 1 is convenient in some situations, e.g. the Binomial > Theorem cannot calculate the probability that you get zero successes > in zero trials unless you define 0^0 = 1. > > However, going from "it is sometimes convenient" to define 0^0 = 1 > to insisting that this should be a general definition seems a bit of > an unjustified leap.
It is convenient generally, not just sometimes.
> Particularly if you use b^(n+1) = b^n / b as your basis for claiming > that b^0 = 1 and b^-1 = 1/b, when that clearly doesn't apply when b > = 0.
That is not used as a justification for defining 0^0. It is used as a justification for leaving 0^0 undefined, even though it does not apply in that case.