A Notation Question (raising the highest value in pow-tower to a different power)

[Micah]

\( \exp^{3}(x) = \exp\(\exp\(\exp(x)\)\) \)

Using the notation that you discuss here, I believe that the function I am curious about may be represented more elegantly by using the notation for it shown below: 

\( f(z,k,r) = \exp_z^k(-r) \) 

Here the z subscript denotes that the base of the exponentiation in this case is the real valued z.  If I were to expand the above function would the notation equate to the following? 

\( f(z=2,k=2,r=1) = 2^{2^{(-1)}} \) 

Thanks for the discussion, and advice on inserting TeX properly. 

-Micah