Perhaps it’s not the most clear, but that absolutely is the standard convention for how to treat exponents, because it results in much simpler shorthand for writing things like this:

https://en.wikipedia.org/wiki/Taylor_series

Example on that page:

-x-(1/2)x^2 -(1/3)x^3 -(1/4)x^4 …

Using your definition you’d have to put a bunch of parenthesis: -x-(1/2)(x^2 )-(1/3)(x^3 )-(1/4)(x^4 )…

And believe me physicists would hate you if you made them do this because they’d have to do it constantly.