repeated or iterated exponentiation

Tetration is the hyperoperation which comes after exponentiation.[1] means y exponentiated by itself, (x-1) times.[2] [3] [4] List of first 4 natural number hyperoperations:

  1. Addition
    a succeeded n times.
  2. Multiplication
    a added to itself, n times.
  3. Exponentiation
    a multiplied by itself, n times.
  4. Tetration
    Note (operator associativity):
    a exponentiated by itself, n-1 times.

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


For the example, addition is assumed.



  1. "Google Answers: addition, multiplication, exponentiation, then ???". Answers.google.com. Retrieved 2011-11-02.
  2. Daniel Geisler. "tetration.org". Tetration. Retrieved 2011-11-02.
  3. "Power Tower - from Wolfram MathWorld". Mathworld.wolfram.com. Retrieved 2011-11-02.
  4. "The Fourth Operation". Retrieved 2019-09-11.