If you are doing it like i think you are, with big numbers, raising them to a power and multiplying them is not O(1), because they are no longer stored in a 32 or 64 bit integer.

I don't know if this kata has been done before but i have one.
It's making a function that calculates the result of a ↑(n) b,
the hyper-operation of order n between a and b.

a ↑(1) b = a + b
a ↑(2) b = a * b
a ↑(3) b = a ^ b
and so on...

taking into account that
a * b = a + a + ...(b times) + a, and
a ^ b = a * a * ...(b times) * a