We can use the following to add the number $2$ to itself $5$ times.
$$f(n,k) = \sum_{x=1}^k n = n\cdot k$$
$$2 + 2 + 2 + 2 + 2 = f(2,5) = \sum_{x=1}^5 2 = 2\cdot 5 = 10$$
We can use a similar strategy for multiplying the number $2$ by itself $5$ times.
$$g(n,k) = \prod_{x=1}^k n = n^k$$
$$2\cdot2\cdot2\cdot2\cdot2 = g(2,5) = \prod_{x=1}^5 2 = 2^5 = 32$$
How could I define $h(n,k)$ such that $h(2,5) = 2^{2^{2^{2^2}}}$?