Absolutely true.

a^0 is 1 for all a , except a=0.

The reason for this definition is to g

comply with the formula a^m / a^n = a^(m-n) .

when m=n   a^m / a^m = a^(m-m) =a^0

but a^m / a^m =1   for any a , safe a=0 .   0/0 is undefined.

NB What about the puzzle ? It is in the trick section , not math!!