Nope, you can’t assume the - is included in the square if there’s no parenthesis around it. The answer is -9.
Surely that would mean the answer’s ambiguous, no? The lack of brackets means we can’t know definitively if - is included or not. But separately, I’d argue that -3 represents negative three, not subtract three, and negative three is it’s own distinct number from positive three.
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.
Surely that would mean the answer’s ambiguous, no? The lack of brackets means we can’t know definitively if - is included or not. But separately, I’d argue that -3 represents negative three, not subtract three, and negative three is it’s own distinct number from positive three.
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.