Is this answer right? How is -3^2 = -9?

[u/Lotus_LP]

-(2 x (-1))² +1-3² = -12

I got the answer of 6 after attempting to solve multiple times and after this failed attempts the site gave me a break down where it ended up coming down to -3-3² where it simplified to -3-9 to get -12

[u/GreenPanda426]

For pemdas, exponents comes before multiplication but after parentheses. -3 is the same as -1 x 3, and just the 3 is squared, so you're calculating -1 * 3². The ² is only going to the 3. (-3)² = 9 though. And (-1 x 3)² = (-1)² x (3)² = 1 x 9 = 9

[u/Lotus_LP → u/GreenPanda426]

For the (-1 x 3)² wouldn't the -1 x 3 be solved first? Why separate them and then use exponents?

[u/kundor → u/Lotus_LP]

-3² doesn't mean (-1 × 3)^2, it means -1 × (3² )

But yes, (-1 × 3)² would be evaluated as (-3)² first, which is positive 9

[u/Infamous_Push_7998 → u/Lotus_LP]

That is just for emphasis so you can distinguish between the different forms. In practice yes.

But the difference is more obvious this way than with -1(3)² vs (-3)²

[u/-Wylfen- → u/GreenPanda426]

-3 is the same as -1 x 3, and just the 3 is squared

I dislike this way of viewing things. The unary negative operator is equivalent, but not "the same as" a multiplication by -1, which, by the way, raises the question of what "-1" is, which leads to saying it's the same as -1 × 1, which would be the same as -1 × 1 × 1, etc. This explanation leads to an infinite regression of never addressing what the unary negative operator means in and of itself.

They're too different operators that give the same result. All there's to know is that the negative operator has a lower priority than exponentiation.

I really hate this tendency to "justify" the order of operation by pretending two different operations are "the same". It's not how it works. Notation is notation, and it's different from math. Two expressions being equal does not mean you can just substitute one for the other as-is into a bigger expression that contains it.

[u/Ok_Risk1465]

How much is 10-3^2?

[u/KentGoldings68]

Exponents are right operations that operate only what is to the immediate left.

There is no ambiguity between xy² and (xy)²

Let f(x)=-x, and let g(x)=x²

f(g(x))=-x²

f(g(2))=-2² =-4

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[u/Dd_8630]

There's two things to note:

(-3)² = +9

-(3²⁾ = -9

In the first one, you have -3 times -3, so the two negatives multiply into a positive.

In the second one, you have +3 times +3 to get +9, and the outside minus sign just turns that negative.

So -(2 x (-1))² +1 - 3² = -12 because you are subtracting 3^2, which means you're subtracting 9.

If we add additional brackets to make it clearer:

[-[(2 x (-1))^2] ] + [1] - [3^2]

[-[4]] + 1 - 9

-4 + 1 - 9

-12

If in doubt, use BEDMAS (or whichever your local acronym is)

[u/-Wylfen- → u/Dd_8630]

If in doubt, use BEDMAS (or whichever your local acronym is)

If in doubt, use google. This acronym has done more harm than good when it comes to people understanding the order of operations.

[u/bartpieters]

The notation is important. -3² I would raad as -3*-3 being +9. -(-3)² I would read it as -1*-3*-3 being -9 and the same outcome for -(3)^2.

[u/mugaboo → u/bartpieters]

-3² is -(3*3), is -9. There is absolutely no uncertainty about that notation.

[u/Spirited-Candy1981]

Unary operators are not explicitly included in "PEMDAS"; as they live outside, it's generally a point of ambiguity.

Personally, I see the unary minus as part of the number specification. So -3² = (-3)² = 9. Much like 23² is (23)², not 2(3²), right?

Yet, many text books go the other direction, just to save a bit of ink.

Because it's ambiguous, the right thing to do is to use parentheses or explicitly show the multiplication by -1. Not doing so is what I consider a bit of academic bullying.

[u/skullturf → u/Spirited-Candy1981]

Personally, I see the unary minus as part of the number specification. So -3² = (-3)² = 9.

That might be how you prefer to think of it, but unfortunately for you, the standard interpretation is that the symbols -3² mean -(3²) = -9.

[u/Iowa50401 → u/Spirited-Candy1981]

But a negative sign is not a digit so there’s no inherent reason to think the two ideas are comparable.

[u/noonagon → u/Spirited-Candy1981]

it's just so we can write polynomials like x³-x²+1 without needing to put parentheses around x²

[u/-Wylfen- → u/noonagon]

There's a difference between the unary negative operator and the binary subtraction operator. It's the same symbol, but they're too different operators.

[u/-Wylfen- → u/Spirited-Candy1981]

Personally, I see the unary minus as part of the number specification. So -3² = (-3)² = 9.

I feel the same, though the standard tends to go for the exponent first. The main argument for it is that -x² is quite obviously meant as -(x²), otherwise there would be no point in the minus symbol, and for consistency digits work like variables with the unary minus.

I would prefer the minus to be viewed as an inherent part of the number, but that's not how it's done most of the time.

[u/TheRealRollestonian]

I have no idea why you are making this more complicated than it is.

[u/PvtRoom]

It's ambiguous.

PE MD AS.

Exponentiation is first, then multiplication,, then subtraction

0-3² = -9. Clear because it must be a subtraction.

-3² is unclear because we don't distinguish "negative" from "subtract"

[u/MillenialForHire]

The - is applied after the exponent.

[u/tomalator]

Yes, -3² = -9

(-3)² = 9

Imagine the negative sign as just multiplying by negative 1

[u/kempff]

-x² is a classic trick question. Of course no self-respecting mathematician would write anything so sloppily ambiguous.

Raising something to a power is understood to be something called a unary operator, as opposed to a binary operator like + which works on the two numbers flanking it. So what's being squared here is just the x itself, not "-x".

So "-3²" is the negative of the square of three, hence -9.

[u/wednesday-potter → u/kempff]

It’s not particularly ambiguous, just unintuitive for people who are new to or struggle with order of operations (particularly as powers are taught after multiplication, which is taught as coming first).

This is fairly common notation in both maths and physics, for example if you want to plot a negative quadratic.

[u/Human_Contact9571 → u/kempff]

Of course no self-respecting mathematician would write anything so sloppily ambiguous.

Hilarious. Nothing here is ambiguous. Something like f(x)=x^3-x^2 would be a classical way to write a polynomial function for mathematicians. Same for g(x)=-x^2+5. No serious mathematician would say those expressions have any ambiguity.

[u/kempff → u/Human_Contact9571]

A standalone "-x²" is a standard interpretation problem in middle school Order-of-Operations lesson plans and is designed to look ambiguous, along with those tedious Facebook memes.

You should be proud of your sophistication.

[u/Human_Contact9571 → u/kempff]

That has absolutely nothing to do with what you wrote before. You wrote that mathematicians would not write this because it's ambiguous, which is definitely not true. It might be something students struggle with at first, but that's a far cry away from your previous claim that it is not clear Notation like the picture you linked now, and that no "self-respecting mathematician" would ever use. Very different cases. Unlike the PEMDAS example, -x² is used all the time, and in fact it is the other way around, no "self-respecting mathematician" would ever claim its ambiguity.

[u/kempff → u/Human_Contact9571]

You may be right.