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

[sheldonison]

...
\( f(z,k,r) = \exp_z^k(-r) \) 

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? 

\( f(z=2,k=2,r=1) = 2^{2^{(-1)}} \) 
...

The notation I like best for clarity to distinguish from raising powers is something like this; with an optional "\circ" and  with brackets around the iteration count of k.
\( f(z,k,r) = \exp_z^{[\circ k]}(-r) \)