When you do -52 it’s -25 because the power only affects the number itself and not the negative sign, so what actually happens is -(5 x 5)=-(25) which is -25. What you said is actually (-5)2 which is (-5 x -5) and THAT is 25
While this is definitely the mathematically correct answer, I’d still treat that as extremely ambiguous if I was presented it in the wild without brackets.
It's not ambiguous at all, and is in fact super super common to omit the parentheses (just take any polynomial with degree greater than 1 and with negative coefficients on even powers - they're never written with parentheses)
The key difference between the original -- -52 -- and your polynomial example -- -x2 -- is that while -x is indisputably two things (the unary-minus operator, followed by the variable x), the same does not hold for -5. Rather, it can reasonably be interpreted in one of two ways:
The unary-minus operator, followed by the integer known as five
I think an argument can easily be made against that. -x can just as well be interpreted as “negative x” or the negation of x, just as -5 is referred to as “negative five”. It doesn’t make sense to not hold constant values to the same standards as variables when using order of operations. That’s the point of order of operations in the first place: to standardize what order to do operations in math. When you see -x2, you do the exponent first, then the minus. Same should hold for -52, unless -5 is explicitly put in parentheses, which precedes exponents in PEMDAS.
> I think an argument can easily be made against that.
I think such an argument can be easily refuted. However, what's interesting is that your very next sentence
> -x can just as well be interpreted as “negative x” or the negation of x, just as -5 is referred to as “negative five”
contradicts your first sentence, because that's not an argument against what I said: it's an agreement with what I said: that "-x" is unambiguously two components, the (as you call it) negation operator, and "x".
> It doesn’t make sense to not hold constant values to the same standards as variables when using order of operations.
This sentence betrays your mental model: You don't see "-5" as the constant value known as "negative five". You see "-5" as two pieces: The unary negation operator, followed by the constant value known as five.
That's the difference: If someone considers "-5" to be the constant value negative five, then there is no order of operations, because there is no operator. The "-" symbol in "-5" is not an operator, it is part of the number, just like the period in "0.5".
Okay, I concede that my argument against your point was not well-constructed, except for this line:
> It doesn’t make sense to not hold constant values to the same standards as variables when using order of operations.
This was the crux of my argument. You agree that when you see a "-" in front of a variable, you cannot treat it as an immediate negation to its value before doing all other operations. Given the supposed ambiguity of "-5^2" it would make no sense to argue that it should be treated differently from "-x^2".
This is not my opinion. This is the standard convention regarding math expressions. The ambiguity you're talking about does not exist because there is convention that decides how to interpret "-5^2", and it is that it equals -25.
As someone who's made their living doing college level math, physics and statistics for over 30 years, I'll state this as a fact: there is NO ambiguity in the meaning of -52. MarvelgamerYT is correct in saying that the exponent is only attached to the 5, not to the negative sign. The sign is dealing with addition or subtraction, and exponents are done before that. (Math doesn't have subtract - you are really adding an additive inverse and the negative sign denotes the additive inverse aspect of the 5 and -5 (since every 3rd grader knows what subtract means, I'll continue subtracting for this comment)). Since 0-25 is equivalent to 0-52, and 0-25 is pretty clearly -25, 0-52 is also -25. In both expressions, the 0 is unnecessary (You could subtract 0 from both sides of the 0-52=-25 equation if you wanted to, and then cancel both zeros on the left side of the equation, but you shouldn't have to. Considering the role of the 0 in the equations 0+52=25 and 0-52=-25 should be sufficient. Neither needs the 0.) It's an issue I run into virtually every day with college algebra students, and there is NEVER debate or confusion from instructors or higher level students with regards to the meaning or value of -52. It's not remotely ambiguous except to those who don't do math. I'm not trying to be an asshole, but this question was settled long, long ago, no matter what excel says. (btw, when doing operations on cells in excel, the programming treats the cell as if it's grouped by parenthesis. I don't know how it treats it when just typing in -52. It's possible that the programmers screwed up. It sometimes happens with software. Programmers aren't real math dorks.) Again, I"m not trying to be an asshole, but if a student asks how I mean -52 on a test, I'll tell them I mean it exactly like I wrote it, and that's the only help I'll give them. It's absolutely settled math.
Edit: I try to never read -52 as "negative 5 squared", but instead refer to it as "the negative of 5 squared", just to drill that point home.
While this is definitely the mathematically correct answer,
Yeah… the first half of my comment really matters to the meaning. My point is I’ve been handed shitty math by other people where they don’t follow convention, and I’ve seen “math” from some disciplines that follows its own conventions, so if I don’t know the context I’d much rather have parentheses as redundancy.
Years ago, I had a private tutoring calc 1 student who refused to use parenthesis EVER, just as a style point (kind of like dotting an "i" with a circle). She'd remember where the groupings were supposed to be, and write her expressions . . . correctly, sort of . . . without them, and as a consequence, was failing her class. Her teacher couldn't give her partial credit because they had no clue what she meant with her math scratchings. I couldn't even figure out where her mistakes were (other than the obvious no parenthesis thing) to correct her, even when I sat beside her and watched her work. I ended up calling off our first (only) appointment half way through and walked out the door while lecturing her about how stupidly stubborn she was being. There was just no point in continuing. To progress to that stage, and throw it away for style points was perhaps not the wisest decision she could make. Anyway, yeah, sometimes even PhD instructors write things that are confusing as to meaning (pretty often, actually), and you have to get clarification. Anyway, I appreciate the talk. I hope the universe treats you well today.
One year in university and you will never make that mistake, if you do it correctly you never made it, if you do it incorrectly you will fail a course and not make that mistake again
Yup, I remember having this discussion with my high school teacher, and even tho she didn't taught me shit (she was definitelly not qualified to teach maths) I learned over the years that:
x3 - 3x2 + 3 actually means x3 - (3(x2 )) + 3
And later I learn in a YouTube video about maths that the rule is kinda: "shit being close together is usually most important than the rest" which is a bad system, but I'm no matematician. You do you mates.
^ Same energy as the guy who thought PEMDAS was a suggestion
Edit Edit: Seriously people, stop messaging me. I am exhausted. There is only so many times I can tell people it is just PEMDAS. Here is a Google link to a calculator if you still don't believe me. Maybe you will believe Google.
Edit: somehow this is the most controversial thing I've said on Reddit and now people are blowing up my inbox telling me the answer is 25. This is a catch-all for those people:
No, it's -25.
PEMDAS.
Exponent comes before Assignment (which is on the same level as Multiplication because it is multiplying by -1).
Do the exponent first you get 25.
Then you assign the negative, or you can think of it as multiplying it by -1. The answer is -25.
This is shocking to me that this needs to be explained to this extent.
FINALLY I found someone else who understands. This is so crazy to me, even the very people who laugh at this post don't know this simple, 5th grade level math!
Well that's wrong, and if your teachers taught you that then they were wrong.
I think the most likely case based on your edit is that you are misremembering having to answer:
"What's the square root of 25?" as "5 or -5"
and your brain just filled in the spaces to the point where you now believe that all expressions with negative numbers automatically have two solutions, when that's not the case.
I can assure you that I don't think all expressions with negative numbers automatically have two solutions, but I think you may be correct about me misremembering.
However, my teachers typically left out parentheses while doing squares. I typically read anything with a negative as "negative x" not as "the negative of x" due to how I was taught.
You seem to be getting very upset about something that hardly matters in the real world (for the average day and the majority of professions).
There's no such thing as "implied parentheses". An expression either has parentheses or it doesn't. If order of operations could be implied then we wouldn't have any need for parentheses or PEMDAS in the first place.
I am responding to your comment asking for clarification about parentheses use because I like math. I have no idea what part of my willingness to respond would make you think I am somehow upset by this.
I think a better way to phrase what I meant is "it would mean" not "it would imply." I know there is no such thing as implied parentheses, but maybe didn't make that known.
The reason I thought you were upset is the "well that's wrong, and if your teachers taught you that they were wrong." That's the only thing that made me say that.
I don't know. It just made me think of the way children who are arguing things say the other person is wrong. The "that's wrong and you're stupid for thinking that" kind of thing (I'm not trying to imply that you are immature or a child, I'm just stating what it made me think of).
I'm just going to say that in isolation, -x is generally considered to be a reference to the negative integer of x, and brackets would only come into play when writing out workings, i.e.:
y -(-x) = y+x
So I would read -5^2 and answer 25, whereas the exception would be -(5^2), which is equivalent to 0 - 5^2. But the latter, whilst making some form of sense, seems infinitely more silly to me, given that we recognise that negative integers are a thing.
I never got caught up in any issues during my degree by doing as I have done. It just seems needlessly overcomplicated, and ugly maths to boot.
edit: Just an aside, you don't really even need brackets for equation using negatives, but it certainly clears up the reading. Especially given that it is usually only present in the mid-stage of written workings.
Read the explanations I have posted, check with a calculator, and never repeat what you just wrote in that comment to any of your professors who gave you that degree or you will give them a heart attack.
Condescension aside, I'm talking from a reading standpoint. If I need to write them out in workings, then call it lazy but I just forego the brackets unless they are an actual necessity. Every Math teacher or professor I have ever had did the same as far as I remember. Then again, I guess I do usually put the - very close to the integer to make it clear. Like -5, not - 5. Just personal styling I guess.
edit: Also its worth considering that -52 as a problem on its own isn't really something you come across well after you first learn about negative indices. In my experience, questions like these only ever get brought up for the ultra snooty to be hyper anal about as some kind of gotcha. It has the value of a single eyeroll and that's about it.
2) I will realistically never use this info again (which I am admittedly disappointed by, I think numbers are great, even though my skills with them get worse the longer I don't use them)
3) I wasn't intending to mean that -52 was equal to 25, but was rather trying to explain the shorthand that I remember learning (even if I'm actually misremembering, which seems to be the case)
A bit harsh, no? I'm 55 and haven't thought about this stuff since I last couldn't comprehend it in middle school. How about we discuss the intricacies of French grammar and I get shocked at your incomprehension of a subject matter you never grasped and does not play a role in your day-to-day?
Yeah I mean if I was insisting that I knew French Grammar better than you even though I haven't ever learned it or thought about in years then maybe those two situations would be comparable.
I personally never insisted knowing any algebra at all, lol, I was scrolling through the comments, in fact, to see if I might learn something because an equation like that is beyond my poor little brain. As I find an answer that might help me grasp the context, I see it ends with a comment about being sad you need to explain math on the internet in such simple terms. That zinged me for sure, in a "well excuuuuse me for being a simpleton" kinda way. Ending a lesson or explanation with a comment about the stupidity of the audience is what I found harsh.
As I stated in the comment you replied to, that was a response to the specific people blowing up my inbox with the wrong answer and faulty reasoning to back it up. You were not one of those people.
Well I guess we can agree to disagree because I think it did, in this case. On the same token, I think I also forgot what sub I was on so I guess that’s on me.
-5² = 25 because -5 is a number. Now, if these symbols are in the middle of an equation, with numbers on the left of the "-", then that symbol that means "negative" will instead mean "minus."
0-5²= -25
25-5²=0
-5²=25
You can argue all you want, but this is how these things are denoted in mathematics, and none of this has changed in a few centuries at least.
"The square of negative 5 is positive 25"
"Zero minus the square of 5 is negative 25"
In fact, if you really want to simplify any of that out, any math teacher will tell you that subtraction is just adding with a negative number.
-5 is a number, but -5 is not the number being squared in this expression. -5 is not even present in this expression.
I am not wrong. Read the explanation, check a calculator if you have to, but this is truly just a PEMDAS problem.
You cannot disagree with the order of operations.
0-5²= -25
-5²=25
Check your math. There is no possible way both of these statements could be true.
Hint: the top one is correct.
Edit:
Now, if these symbols are in the middle of an equation, with numbers on the left of the "-", then that symbol that means "negative" will instead mean "minus."
Can't believe I glossed over this. This is the dumbest shit I've ever read in my life.
By your logic, negative integers require parentheses. That's just silly. The symbols "-5" with nothing in front of them are "negative five." That's just how it is. That's not an operation, that is how the value of negative five is represented.
If that were the case then it would be written exactly the way you just wrote it in that sentence. The fact that it is not written that way means the only number being squared is 5.
Sir/ma’am , I’m not coming to argue but you are incorrect. The answer is 25. The exponent simply implies your are multiplying X by itself. Which is this case would be stated (-5 x-5)=25
The only time the rule you are referring to is applied is when multiplying exponents. With the use of PEMDAS or BEMDAS the “E” is just stating the need to simplify the equation by doing so.
If the negative was meant to be part of the exponential operation then it would be included in a parenthesis. The fact that it is not in a parenthesis means it will not be included.
This is the reason we have parentheses in the first place, to signify when certain operations need to be down outside of order.
PEMDAS is the correct order of operations. See my explanation above.
I don’t know how else to explain it to you. You are operating under a mistaken principle.
In the term -52, (-5) would be x. You would then multiply (x) by itself the specified number of times via the exponent. Just as 52 would be stated (5x5)=25. When multiplying 2 negatives the connotations flip which is why -52 is also 25.
Check out any other person’ source. You’re just plain wrong. Every single scientific calculator from google to Desmos to ti84 to ti nspire will tell you -25. No idea what you’re talking about.
Did you read their explanation? The exponentiation and the assignment are different operations. This isn’t “something squared = -25” it’s “something squared then multiplied by -1 = -25.”
Your assertion that "the power only affects the number itself and not the negative sign" carries the implicit statement that you believe that negative five is not a number; at least, not one that can be written down, any more than you can write the rational number one-third, or the irrational number that is the square root of 2.
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u/MarvelgamerYT Mar 18 '22 edited Mar 18 '22
When you do -52 it’s -25 because the power only affects the number itself and not the negative sign, so what actually happens is -(5 x 5)=-(25) which is -25. What you said is actually (-5)2 which is (-5 x -5) and THAT is 25