-9^2 = -81

@PurpleDaisies Interesting that you have a physics degree. I do, too, but mine taught me to be open-minded and curious, and to look at things from alternative angles, rather than to tell people they 'are just wrong'.

If you bother to look online, you'll see there's lots and lots of discussion about this very topic, with an acceptance that there will never be a entirely definitive answer - but the general consensus is that the OP is correct.

Out of interest, how would you treat the coefficient -x2 if it were the leading term in a polynomial? As -(x2) or as (-x)^2 ? And do you think the unary operator is treated differently in an algebraic expression than in a purely numerical one?

I passed Maths , O level before bidmas, if an exam board wanted you to do something first they put brackets round it.
I actually think computers have made maths sloppy.
Maybe it is time they were made compulsory in exams.

Just asked ds age 9 this he said 81. We did it on my iPhone calculator and a normal one and got -81 and 81.

He’s going to ask his maths teacher tomorrow.

Maths PhD here popping in. An actual, genuine one, in pure maths. Sorry don't have time to type out a proper explanation (sick kids), essentially BiDMAS or whatever acronym you prefer as convention is exponent attaches itself to what immediately precedes it, but -9^2 is definitely -81. I'm quite shocked that anyone with a maths or physics degree would think otherwise tbh!

Does this imply that negative numbers should be in brackets to distinguish them from positive numbers?

so -9 is assumed to be 0 minus 9 where as (-9) is negative 9?

noble So we're ALL right?

How would I talk about it to a class?

“I have the number ‘minus 9’. I want to square it. This means multiplying it by itself. So if I square ‘minus 9’ I do ‘minus 9 x minus 9’ which is ‘positive 81’. So ‘minus 9’ squared is ‘positive 81’

Remember if you do this on your calculator put brackets around the ‘-9’ so that your calculator knows you’re squaring ‘minus 9’ and you don’t want to subtract 9 squared as that is minus 81 due to BIDMAS.”

Less confusing if you call minus 9 ‘negative 9’.

The calculator rigidly applies BIDMAS and needs the brackets. Kids do not rigidly apply BIDMAS, and would assume that -9^2 was ‘minus 9 squared’, especially if they’d had it hammered into them in the lesson that squaring a negative gives a positive.

Maths tests, teachers and textbooks should really put brackets around the -9 when squaring but can be sloppy. Kids usually don’t.

Technically the answer to -92 is -81, but in a school setting, I’d have guessed that the answer is meant^ to be 81.

Bold fail!

I love WolframAlpha!

@StealthPolarBear
I know what the answer is grin I also have a maths degree.
I'm just showing that it is equivalently stupid to -9^2 = -81

It’s not equivalent at all. Everyone knows the + and - in BIDMAS are of equal value. An index is always done before a + or - unless there are brackets. Your examples are not comparable.

The correct answer is the one that the examining board are looking for either its either minus nine squared or the negative of nine squared. Which one does the examining board say it is? You don't need to agree you just need to do.

If someone showed me -92 I'd think it was minus nine squared rather than the negative of nine squared. If your education board say you ought to think of it as the negative of nine squared then thats what you need to start thinking to get your kids through the exams. Makes it odd if you now have to write minus nine squared as -(92) all the time.

There you go...

Bidmas....
There are no brackets.
So you do the square bit next.
Then you apply the negative.

Put it into WolframAlpha. -9^2 is -81

All the YouTube videos say unless the number with the minus is in brackets you do the square then apply the negative number.
So yes answer is -81.
I am old so I got it wrong.

@CharlieWork

-9^2 is definitely 81.

It really isn’t! -9 x -9 = 81 but -92 is -(92) = -(9x9)
(-9)^2 is -9x-9 which of course is 81.
They are not the same.

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.

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.

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.

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.

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.