Deriving tetration from selfroot?

[Ivars]

Besides I think you forget several parens in the above quote, the convention is that if there are no brackets for exponentiation then the brackets are to the right side. 3^3^3 := 3^(3^3). What you meant was probably
(((3^3)^3)^3)^3=3^(3*3*3*3)=3^(3*3^3)=(3^3)^(3^3)=27^27

Thank You;So balanced tetration is something in between repeated exponentiation from left and tetration.
Yes, I left brackets out thinking convention is from the left. But I meant what You write, exactly.

Ivars