The ancient Babylonians understood squares:
The ancient Athenians understood cubes, if we can take doubling the cube, i.e., the Delian problem, as evidence.
My question is:
Q. When were 4th, 5th, $\ldots$, $n$-th powers contemplated/understood/used?
I am wondering how tied was the understanding of powers/exponentiation to geometry, to spatial dimensions. Did the ancients generalize their explorations to arbitrary integer exponents?
