It's -(3^2) that's the rule right??
this post was submitted on 19 Jan 2025
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No, PEMDAS.
You do the exponent first, then multiplication.
-3² = -1 * 3²
or
-3² = (-1)(3²)
(-3)² would be how you'd represent what you are interpreting it as.
Your interpretation:
-3² != (-3)² = (-1(3))² = (-1 * 3)² = 9
vs
Correct Interpretation:
-3² = -3² = (-1)(3²) = -1 * 3² = -9
EDIT:
Every time you see a - directly infront of a number, say...
-x
...and there is no space to indicate the - represents a subtraction operator, such as in...
y - x
...the immediate prefix - actually represents:
(-1)x
or
-1 * x
Due to PEMDAS, if the exponent ² or ^2 is attached to...
-x² or -x^2
... this actually represents
(-1)(x²) or -1 * x^2
... such that PEMDAS is upheld, and the exponent recieves computational primacy.
EDIT 2:
I don't make these rules, but this is how it works.
Double check in wolfram alpha if you doubt it.
(-3)²
Well, in my defense, that's has the uglies.
Correct, or, -1 x 3^2 Joke is democracy doesn't always get it right
I figured. I just had to check if I had gone mad
I would say it's -3 × -3.
Nope, you can't assume the - is included in the square if there's no parenthesis around it. The answer is -9. Think of it like "0-3²" which is more obviously -9.
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:
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 x^2^ where x = -3, I don't think you'd say it's -9.
the worst order of operations thing imo is with the denominator in division, many people say that 1/4x should be read as (1/4) * x and not 1/(4x), although I think this is usually the less popular option in polls
apparently wolfram alpha does it that way, as well as most newer graphing calculators (TI switched between the ti-82 and ti-83)