I have a Casio fx-115MS, it shows 2^3^2=64. It should be 512. By the way, can you do the same for (...((x^x)^x)^...? if you can, the result would be the same although they are two different problems.
I used TI-89 calculator to compute (2^0.5)^(2^0.5)^(2^0.5)...and have not made it passed 2.
Happy New Year to you.