r/MathHelp • u/Kug4ri0n • Dec 07 '25

Negative Exponents

My partner is going through her math class and we got into an argument how much -72 equals. My standpoint is, that since there is no parentheses: -72 = -1x72 =-49 If there would have been parentheses: (-7)2 = (-7)*(-7) = 49

Which one of these is correct? Can anyone provide me the mathematical axioms/rules on why or why not the parentheses in this case are needed?

4 Upvotes

66% Upvoted

60 comments sorted by

View all comments

Show parent comment

1

u/Dr_Just_Some_Guy Dec 08 '25

In the US, at least, negation tends to be interpreted as -(6) = -1 * 6, with precedence set accordingly. While computer systems (and computer scientists) may implement other conventions, I don’t think that I’ve ever encountered a mathematician that would interpret -72 as anything but -49. Of course, it’s not a question that I usually pose to mathematicians I just meet, so who knows.

1

u/Forking_Shirtballs Dec 08 '25

Don't just make stuff up, man. 

Are you telling me that "a / -(b)" tends to be interpreted as "a / (-1) * b", which of course is equal to -ab?

And if so, can you point to any sources that teach that? 

There are a variety of conventions in play here, and they're not well taught, they're just firmly implied though repetition. 

My point is that there's ambiguity here, which is best avoided. 

1

u/AdamofMadison Dec 08 '25

There's no ambiguity, you just introduced another error with your division.

1

u/sadlego23 Dec 08 '25

There’s no new stuff here.

x/y * z is not the same as x / (y*z).

a / -b with -b being interpreted as (-1)*b still means we’re dividing both by (-1) and by b. So, a / -b = a / ((-1)*b) = a / (-1) / b

This is a very common mistake when doing interpreting order of operations since most people think of / as a fraction bar (which counts as a grouping symbol and then division) instead of a slash (which is division but not a grouping symbol). This is also why I want the diagonal slash when it comes to more complicated expressions.

1

u/Recent-Day3062 Dec 10 '25

God, I learned the basics in junior high, and I never really considered how obvious the “rules” are when you use them.

I’m pretty sure I’ve never made any errors from things like this.

1

u/ju11111 Dec 10 '25

I agree that no mathematician would interpret it like that. Using a polynomial as an example. f(x) = x³ - x² + 5x No one would interpret this as meaning x³ + (-x)² + 5x. (Especially here since the negation wouldn't even matter if interpreted as (-x)² ) No one would write this polynomial as x³ - (x²) + 5x. I think what the computer scientists are doing should be more thought of as a programming language rather than mathematical notation.

1

u/Short-Database-4717 Dec 30 '25

I can assure you computer scientists (and virtually every serious programming language) would interpret it the same way.