For ten points, name this process of iterated exponentiation, a function also referred to as hyper4 or "power tower".
This function can be extended to complex numbers with integer coefficients, but not to the real numbers, because unlike its predecessors the field operations, it is nonassociative. Notated as two Knuth arrows or a Conway chained arrow, it's the next member of the sequence "addition, multiplication, exponentiation, et cetera". For ten points, name this process of iterated exponentiation, a function also referred to as hyper4 or "power tower".
This function can be extended to complex numbers with integer coefficients, but not to the real numbers, because unlike its predecessors the field operations, it is nonassociative.
{Tetration} [accept "hyper4" or "power tower" before mention;  prompt on "iterated exponentiation" before mention]