This will have to be my last comment on this side discussion, not because it is not interesting (it deserves its own thread) but because I do not want to hijack the original question.
@jerv
With regard to Polish notation, I find that once you get the hang of it, it can be less confusing than entering parentheses. (2+3) * (4+7) can be a bit confusing to enter sequentially, especially if you don’t have a graphing calculator, whereas 2 3+4 7+* is not as bad.
@lapilofu
Technically speaking, 4*3 is not the same as 3*4. The second term is called the multiplicand and it is what gets multiplied by the first term, called the multiplier. I admit that this is a little pedantic, since both expressions have the same value and the distinctions break down when you get beyond integers. Still, it does show that there is an inconsistency with exponential notation, where, as you point out, order makes a difference since the operation is not commutative.