I think that an exponent of zero being equal to 1 is an empirical choice that allows a function like a^x to be continuous at x = 0.
If you are familiar with infinite power series then you know that the series for e^x yields the value 1 for x = 0; and because all the terms in x vanish at x = 0, the result is exact.
This argument is hueristic and lacks rigor but it's the best I can do in my bathrobe.