Having done some searches on the internet, seems like the term "power" is a mistranslation. The Wikipedia article links to an article in the MacTutor History of Mathematics archive where it is written
The notation and terminology for powers and exponents is interesting. Power is first used for the square. Euclid uses the phrase in power , for example he says that magnitudes are commensurable in power when their squares are commensurable. Of course Euclid thought geometrically and the square to him was the geometrical square not a new number formed by multiplying the number by itself. Henry Billingsley, the first English translator of Euclid in 1570, makes the definition precise in his translation of Euclid's Second book:- The power of a line is the square of the same line.
Are these the intended meanings? For the first instance (concerning commensurability) -
εὐθεῖαι δυνάμει σύμμετροί εἰσιν, ὅταν τὰ ἀπ᾽ αὐτῶν τετράγωνα τῷ αὐτῷ χωρίῳ μετρῆται
I could not find the corresponding place in the Book 2 for Billingsley's translation.
I would translate "δυνάμει" in the above context as "potentially", which must be closely related to "δύνατον" ("possible") frequently used across Euclid's books. Cf. German "Potenz" for "power".
Thus although "potence" is sort of a synonym for "power", that another meaning of potentiality is lost when using "power" I think.
Is my interpretation correct? Are there any authoritative opinions on this?