We can define 2^3⁴ either as (2³)⁴ or as 2^(3⁴) . Does it make any difference?

Now calculate (Ö(2)^Ö(2))^Ö(2) and Ö(2)^{(Ö(2)^Ö(2))} and answer the following question for both definitions.

Which number is the biggest

Ö(2)^{Ö(2)^{Ö(2)^{Ö(2)^{.^{.^.}}}}}

where the powers of root 2 go on for ever, or

(Ö(2)^Ö(2))^Ö(2) ?