Ivars Wrote: 3^3^3^3^3 = 3^3^(3^3) = 4,43426E+38 = 27^27
2^2^2^2^2= 2^(2^(2^2) = 65536
So 5 times exponentiated 2 =2[4]4; But 5 times exponenetiated 3 equals something that has no name -at least I do not know it -
we call (x^x)^(x^x) balanced tetration, though I think there lacks still a symbol, so I use here [4B]:
x[4B] 2 = x^x
x[4B] 4 = (x^x)^(x^x)
x[4B] 8 = ((x^x)^(x^x))^((x^x)^(x^x))
Generally
x[4B] 1 = x
x [4B] 2^(n+1) = (x [4B] 2^n)^(x [4B] 2^n)
The topic was not really discussed yet on this board however, already mentioned in this posts: post1, post2.
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