Tetration

Tetration is the hyperoperation which comes after exponentiation.  means y exponentiated by itself, (x-1) times. List of first 4 natural number hyperoperations, the inverse operations of tetration are the super root and the super logarithm.
Addition

 copies of 1 added to .
Multiplication

 copies of  combined by addition.
Exponentiation

 copies of  combined by multiplication.
Tetration

 copies of  combined by exponentiation, right-to-left.

The above example is read as "the nth tetration of a".

 Examples 



{| class="wikitable"
! 
! 
! 
! 
! 
|- align=right
| 1
| 1 (11)
| 1 (11)
| 1 (11)
|  (11) (Absolute infinity and Infinity)
|- align=right
| 2
| 4 (22)
| 16 (24)
| 65,536 (216)
| 
|- align=right
| 3
| 27 (33)
| 7,625,597,484,987 (327)
| 1.258015 × 103,638,334,640,024
| 
|- align=right
| 4
| 256 (44)
| 1.34078 ×10154 (4256)
|  (8.1 × 10153 digits)
| 
|- align=right
| 5
| 3,125 (55)
| 1.91101 × 102,184 (53,125)
|  (1.3 × 102,184 digits)
| 
|- align=right
| 6
| 46,656 (66)
| 2.65912 × 1036,305 (646,656)
|  (2.1 × 1036,305 digits)
| 
|- align=right
| 7
| 823,543 (77)
| 3.75982 × 10695,974 (7823,543)
|  (3.2 × 10695,974 digits)
| 
|- align=right
| 8
| 16,777,216 (88)
| 6.01452 × 1015,151,335
|  (5.4 × 1015,151,335 digits)
| 
|- align=right
| 9
| 387,420,489 (99)
| 4.28125 × 10369,693,099
|  (4.1 × 10369,693,099 digits)
| 
|- align=right
| 10
| 10,000,000,000 (1010)
| 1010,000,000,000
|  (1010,000,000,000 digits)
| 
|- align=right
| ∞
| ∞∞
|  (∞∞∞)
| 
| 
|}

 References 

Category:Hyperoperations