-9^2 = -81

[insufferablefury]

I need a help from maths teachers.

My dc says her teacher taught the children the answer is 81. And when she has done the work on online maths programme, it's wrong obviously.

I have explained, it's -81, since it's really - (92). And to get answer as 81, the question need to be (-9)2, not -9^2. But being not a maths specialist, cannot explain why in a logical way , and the child blatantly believes the teacher, which is a good thing, but not really if the teacher is wrong.

How do you maths teachers explain this to your students?

StealthPolarBear, I have seen your past post and kind of respected you. But what you are doing here, no. I had genuine question. And I had great answers. Just because you don't get it, it's pathetic to take a mickey about it. Very disappointed.

So, all these people are taking mickey out of me, because I am stupid to think -9^2 = -81. Ok,
How sad that people who are teachers think I am wrong....

@PurpleDaisies

It’s the numeral -9 raised to the power 2. That is 81.

Or, it’s the negative of the result of 9 raised to the power 2, which is what the accepted convention of the orders of operations gives you.

You could equally consider the use of the minus sign as:

(-1)*9^2

Again, the exponent takes precedence over the multiplication and so the answer is -81.

What people are arguing is that the minus sign doesn’t attach itself to the numeral, but to the result of which ever operation has precedence, by convention.

The square of a negative number is always positive. There are no imaginary zeros at the beginning of an expression.

Get her to ask whether the intention is to square negative 9 or multiply the square of 9 by negative one. I reckon brackets will appear in subsequent questions.

@TeenPlusTwenties, I don't think I m wrong to think -9^2 = -81. Am I? I assume you have maths knowledge, could you help?

How sad that people who are teachers think I am wrong....

You are wrong. You are just wrong.

If you were right, you could square root -81. You can’t without using imaginary numbers.

If you want to view -9 as a subtraction from zero, the equivalent equation isn't 0 - 9^2.

It's (0-9)^2. Which has to be solved by multiplying out

(0-9)*(0-9)
= (00) + (0-9) + (-90) + (-9-9)
= 0 + 0 + 0 + 81
= 81

TheFallenMadonna, no, she made a mistake, she answered the question as 81, and as soon as seen the question, I knew she was wrong. Question was to answer what was a value of -9^2. The answer was -81

Nothing like a maths questions to bring out a whole host of maths degrees. I’m sure some of them are real too...

-9^2 as a child’s maths question is super unhelpful for learning unless it’s clear what the purpose is. If it’s an exercise to try and push the point that the square of a negative number is a positive then it’s mathematically incorrect. If it’s an exercise of BODMAS it’s difficult (because of the lack of any value between the - and the 9) but I suppose as an extension question it could be clever.

I suspect the teacher was attempting the former but has insufficient understanding of the maths to form a mathematically correct question.

PurpleDaisies, no sorry, I am not wrong. I know it. It's so frustrating to deal with someone who thinks they do know everything. I did respect you too. Really try typing the question on really good calculator, the answer is -81.

When I was a teenager doing maths calculators would calculate -9^2 as 81 but now the same input on both the Casio and Sanyo scientific non programmable calculators 99% my students use calculate it as -81.

I should probably say my degree is physics not maths!

Or, it’s the negative of the result of 9 raised to the power 2, which is what the accepted convention of the orders of operations gives you.

I have NEVER seen this. -92 On its own is always (-9)2 by convention.

OP, I can kind of understand where you are coming from tbh.

The assumption, when faced with -92, is (-9)2, not that you are subtracting from another number.

It is a very strange question in isolation and not including brackets.

If you put it in a calculator you get - 81 because the calculator does -(9^2).

I'd agree with people saying imagine a 0 at the start.

Really try typing the question on really good calculator, the answer is -81.

It isn’t though. You clearly don’t have brought mathematical knowledge to doubt the infallibility of the answer a calculator gives you.

I understand your point. I'm saying that asking the teacher to clarify the intention (which is likely to be squaring the negative, given your daughter's answer) is likely to lead to tighter notation in the future.

insufferable
I'm with you, (but if someone gave it to me I'd be asking where they wanted the brackets).
My GCSE approved Casio fx-85GT Plus calculator thinks -81 too.

You need @noblegiraffe and I expect @DadDadDad would like to express an opinion too.

There isn't actually a 0 in front of the -9, of course not. It's just a shorthand way of explaining the convention of why, when there are no brackets, you do the exponent first to the positive integer of 9 and then the negation. Hence the right answer for the OP's question is negative 81 when no brackets.

If there had been brackets around the -9 then you treat it as a square of the number -9 and get positive 81.

That is the whole point. The question was -9^2 and answer was -81. And she was wrong, my dc answered 81, thinking -9 x -9 = 81.
For very weird coincidence, I just read a question on maths thread on some forum asking about this exact problem. So I learned as a fact, that negative before number with powers means negative that powered number. I wouldn't have known otherwise.

The - sign before the -9 is not a subtraction sign, it's to denote that the number is negative. So I'm not getting the bodmas argument. -92 has only one operation... and that's the square. There is no subtraction operation. There is no invisible 0. 0-92 is a different question, in which bodmas comes in to play as there are two operations - a square and a subtraction. -9^2 = 81. The square root of 81 can be either 9 or -9.

My comment was to Purple Daisy

There is nothing wrong with writing a deliberately confusing question with the final aim of clearing up confusion afterwards, if that's what is going on.

As previous PPs have said -9^2 mean squaring and then applying the negative hence -81 is what is meant by convention. If you type -9 in a calculator and then square you are changing the order. With old fashion calculators one had to force the correct order. Many of my students did make this mistake that the calculator will take care of Bodmas.

dootball, I don't get you at all. I know the answer is -81, but I couldn't explain logically why, that was a reason I started this thread. I made that clear on my op.
I would love it if @noblegiraffe turns up and clear my confusion.