Isn't this treating 3 as something that can be analyzed from -3? Like -3 is the union of 3 and the (-), and not something onto itself. Ought it to be the case that negative is more than just a sign? Like, I think 3 should be ontologically distinct from -3, even if the addition of 3 and -3 = 0. Idk, I don't have a reason for this, it feels right for some reason.
There is indeed two ontologically different elements 3 and (-3) in Z. The question is however purely about what is the meaning of the ambiguous without precedence rules representation -3^2.
Note that it gets more complicated quickly if you want to keep thinking about it in that mathematicians often consider ontologically different but equivalent operations as the same when it’s irrelevant to what they are doing or the results trivially extend to both case. See for example 3-3 and 3+(-3).
