The ancient Babylonians understood squares:
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<img src="https://i.sstatic.net/U4eqh.jpg" width="360" />
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<sup>[Plimpton 322](http://www.aliraqi.org/forums/showthread.php?p=147847980)</sup>
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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