The whole point of this is that there isn't necessarily a single right answer. As another user pointed out, mathematicians define 0^0 to be 1, but you don't necessarily have to accept that as truth in the way that 1+1=2.
If the calculator is powerful enough (as in the case of Mathematica) to evaluate Taylor series, for example the Maclaurin series for e^x when x=0, then in doing so it implicitly admits 0^0=1. If it simultaneously says 0^0 is not 1, then the calculator is inconsistent. (Mathematica IS inconsistent in this example)