Understanding Tetration

Tetration extends exponentiation by iterating power operations. The notation $a^b$ represents exponentiation; tetration writes $a^b$ again but with the exponent recursively containing a power tower of height $b$. It is sometimes denoted $a^{\uparrow }$ or $a^b$ with a special "tetration" operator.

Formally, for positive integers $b$, tetration is defined recursively by $a^1=a$ and $a^b=a^{a^{b-1}}$. Even for small inputs, results grow extremely quickly.