kingofthenothing
Yeah, I have that problem when I use my calculator. It keeps giving me "1", even when it can say other things are undefined.

TheOtherCapnS
Depends on the context and discipline, and I don't think any mathematician would fault someone for using 0^0=1 when necessary. Except for fucking Cauchy, I mean.

eatuntilidie
You define integer exponentiation by A^B = (the number of functions from a set of size B to a set of size A). 0^0 is the number of function from a set of size 0 (the empty set) to the empty set. There is exactly one such function, and it is called the empty function.

You might say "oh, but the function x^x is discontinuous on (-inf,0], and so 0^0 shouldn't be defined." If you believe this, then you also believe that (-1)^(-1) is undefined, so (surprise), -1 has no multiplicative inverse and hence rational numbers are not a field (oops).