# Manuals/calci/TETRATE

TETRATE(a,n)

• is the base value.
• is power value.

## Description

• This function shows the tetration value of the given number.
• In , is the base value and is the power value.
• The hyperoperation after exponentiation is Tetration.
• Tetration is called iterated exponentiation.
• The notation means $\displaystyle a^{a}^{\cdots }^{a}$ the application of exponentiation times.
• For any positive real a>0 and non-negative integer we define by:

$cases}"): {\displaystyle ^n a = \begin{cases} 1, & \mbox{if }n\mbox{=0} \\ a^{[(n-1)a]}, & \mbox{if }n\mbox{ >0} \end{cases}$

## Examples

1. TETRATE (3,2) = 27
2. TETRATE (4,3) = 1.3407807929942597e+154
3. TETRATE (10,2) = 10000000000

Exponent