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

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

Which number is the biggest

√(2)^{√(2)^{√(2)^{√(2)^{.^{.^.}}}}}

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

(√(2)^√(2))^√(2) ?