Hi dudes, don't be put off by the clumsy notation here. I was wondering about these particular exponent towers and this curious property of theirs... Let p be a positive integer. Then the exponent tower, composed of p+1 parts each of value p^(1/p), equals p. e.g. for p=2. tower part = 2^(1/2) (2^(1/2))^ ((2^(1/2))^(2^(1/2)))=2 bah, this looks clumsy, but it's concise written by hand, i.e. a 3 part exponent tower. Anyway, I heard that it's difficult to prove any particular case for p, let alone the general case. I had a go myself for case p=2. I set x equals exponent tower and tried to show x=2, but I got nowhere. Can anyone post the easiest proof for case p=2?, or any other case?