There are calculus books that say that 0^0 is undefined. The reason for this is tradition; long ago, before continuous functions were well understood, Gauss placed 0^0 in a table of "indeterminate forms", a concept that becomes obsolete once you know the relation between limits and continuous functions.
There are numerous places in mathematics where 0^0 is implicitly assumed to be 1.
So if you want consistency, then 0^0 must be defined as 1.
Some people say that sometimes 0 is better and sometimes 1 is better, but this is not true, the value 0 is never useful, and the value 1 never leads to contradictions.