TITLE: History of powers beyond squares and cubes
QUESTION [25 upvotes]: The ancient Babylonians understood squares:



 
 
 
Plimpton 322

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?

REPLY [18 votes]: The cuneiform tablet MS 2351 from the 19th century BC contains the 15-digit sexagesimal number 13 22 50 54 59 09 29 58 26 43 17 31 51 06 40, which happens to equal $20^{20}$. I also seem to remember they constructed a table of reciprocals for numbers of the form $125 \cdot 2^n$ for exponents up to $19$.
Edit. Last year some fragments of a large table have been identified:
Ossendrijver discovered that the complete table contained the powers of 9 up to $9^{46}$.