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:
It’s been a hot minute since I’ve had to do any serious maths, but that does roughly line up with what I remember about BODMAS. It’s just intuitively, there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3). If you where to solve x2 where x = -3, I don’t think you’d say it’s -9.
there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3).
The only difference is whether it’s in brackets or not. To square the number -3 you need to put it in brackets, otherwise you’re only squaring 3.
x2 where x = -3, I don’t think you’d say it’s -9
That’s because anytime you substitute for a pronumeral, whatever the pronumeral represents goes in brackets. e.g. for x=3, 2x=2(3). So if x=-3, then x²=(-3)², as opposed to if x=3, we have -x²=-(3)². Whatever the pronumeral is equal to is inside brackets when you substitute.
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.
It’s been a hot minute since I’ve had to do any serious maths, but that does roughly line up with what I remember about BODMAS. It’s just intuitively, there’s a difference between - as an infix operator (10 - 5) and - as a prefix (-3). If you where to solve x2 where x = -3, I don’t think you’d say it’s -9.
The only difference is whether it’s in brackets or not. To square the number -3 you need to put it in brackets, otherwise you’re only squaring 3.
That’s because anytime you substitute for a pronumeral, whatever the pronumeral represents goes in brackets. e.g. for x=3, 2x=2(3). So if x=-3, then x²=(-3)², as opposed to if x=3, we have -x²=-(3)². Whatever the pronumeral is equal to is inside brackets when you substitute.