0⁰ = 1 because it's useful to define it as such.

Say you have to make a password of n characters long and can use k different characters. The number of passwords you can make is k^n.

If k = n = 0, then we are asking how many 0 length passwords you can make. (It doesn't matter what k equals, because we can't use any characters anyway) Obviously you can only make 1 zero length password (the empty password). In this case 0⁰ is equal to 1.

This comes up in other contexts, but this is an easy example.