# What is the name for this: “x^^y” (as in 2^^2=2^2 and 3^^3=3^3^3 and so on)

How do you call / is there any specific name for the following:

x^^y

e.g.:

• 2^^2 = 2^2
• 3^^3 = 3^3^3
• 4^^4 = 4^4^4^4
• ...
• superpowers, Knuth notation. – Wuestenfux Dec 31 '18 at 17:31
• Look up "tetration:. en.wikipedia.org/wiki/Tetration – Ethan Bolker Dec 31 '18 at 17:32
• Power tower or tetration springs to mind, also denoted $$^na,$$ where $a$ is raised to itself $n-1$ times. – Antinous Dec 31 '18 at 17:33

This is known as tetration, where $$^na$$ is $$a^{a^{a^{...}}}$$ with $$n$$ copies of $$a$$ in the exponentiation. You might also seen it written as $$a \uparrow \uparrow n$$.