# Tetration

Tetration is the hyperoperation which comes after exponentiation.[1] ${\displaystyle ^{x}{y}}$ means y exponentiated by itself, (x-1) times.[2][3][4] List of first 4 natural number hyperoperations, the inverse of tetration is the super root shown in the example

${\displaystyle a+n=a+\underbrace {1+1+\cdots +1} _{n}}$
n copies of 1 added to a.
2. Multiplication
${\displaystyle a\times n=\underbrace {a+a+\cdots +a} _{n}}$
n copies of a combined by addition.
3. Exponentiation
${\displaystyle a^{n}=\underbrace {a\times a\times \cdots \times a} _{n}}$
n copies of a combined by multiplication.
4. Tetration
${\displaystyle {^{n}a}=\underbrace {a^{a^{\cdot ^{\cdot ^{a}}}}} _{n}}$
n copies of a combined by exponentiation, right-to-left.

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

## Example

${\displaystyle ^{2}3=3^{3}=27}$