The ancient Babylonians understood squares: <hr /> <img src="https://i.sstatic.net/U4eqh.jpg" width="360" /> <br /> <sup>[Plimpton 322](http://www.aliraqi.org/forums/showthread.php?p=147847980)</sup> <hr /> The ancient Athenians understood cubes, if we can take doubling the cube, i.e., [the Delian problem](http://mathworld.wolfram.com/CubeDuplication.html), 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? [1]: https://i.sstatic.net/U4eqh.jpg