tetration
The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ᵇᵃ denoting a to the power of a to the power of … to the power of a, in which a appears b times.
uncountable
⁴²#61;2#123;(2#123;(#123;2²#125;)#125;)#125; #61;2#123;(#123;2⁴#125;)#125; #61;2#123;16#125; #61;64,536
You don't ordinarily hear much about tetration because it is so powerful an operation that tetrating even very small numbers with each other produces inordinately large numbers. A tetration is worked out below.
Where it comes from
From tetra- (prefix meaning ‘four’) + (itera)tion, from the fact that tetration is in fourth place after addition, multiplication, and exponentiation. The word was coined by the English mathematician Reuben Goodstein (1912–1985).
Adapted from the Wiktionary entry tetration (CC BY-SA 4.0).