He asked why 0^0^0=1. I think 0^0^0=0. Here the question is again about association: if 0^0^0=0^(0^0), then because 0^0=1, 0^0^0=0. If 0^0^0=(0^0)^0, then it is 1.... 0^0^0^0=1 is correct. Even/odd