Is there a term (or operation) for repeated exponentiation?
I.e. Repeated addition is multiplication, repeated multiplication is exponentiation, repeated exponentiation is X?
Is there even such a term for such a "higher order" operation, seeing as we could potentially deal with this by increasing the exponent?
The word you are looking for is probably tetration
at least if you are looking for something like $$\underbrace{a^{(a^{(\cdot^{\cdot^{a)\cdots)}}}}}_n$$