- #1

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I know - x - = +

I am told -3²= -9 not +9

-3² means -3 x -3 = 9

I am told (-3)² = 9

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- Thread starter gary350
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- #1

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I know - x - = +

I am told -3²= -9 not +9

-3² means -3 x -3 = 9

I am told (-3)² = 9

- #2

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[tex]3^2=9[/tex]

[tex]-3^2=-9[/tex]

[tex](-3)^2=(-1)^2 3^2 = 1 \cdot 9=9[/tex]

[tex]-3^2=-9[/tex]

[tex](-3)^2=(-1)^2 3^2 = 1 \cdot 9=9[/tex]

- #3

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Or, similarly,

## -3^2=-(3)(3)=-9##;

##(-3)^2=(-3)(-3)=3^2=9 ##

## -3^2=-(3)(3)=-9##;

##(-3)^2=(-3)(-3)=3^2=9 ##

- #4

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in contrast:

##(-3)^2 = (-3)*(-3) = 9## the parens modifies the precedence so that (-3)^2 = (-3)*(-3)

- #5

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My calculator also shows 3²=9

Both make sense because -x-=+

-x-=- makes no sense.

I only know real math symbols, what are ^ & * mean?

I makes no sense to pull a -1 out of the air and put it into a problem that has no -1 in it?

-3² should = -3 x -3 = 9

- #6

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My TI-83+ says

What is the make and model number of your calculator?

What is the make and model number of your calculator?

- #7

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^ and *I only know real math symbols, what are ^ & * mean?

I makes no sense to pull a -1 out of the air and put it into a problem that has no -1 in it?

-3² should = -3 x -3 = 9

^ represents exponentiation: 3^5 is ##3^5##

and

* represents multiplication: 3*5 is ##3 \times 5##.

You see ASCII code all the time on forums like this, when the typist doesn't know LaTeX coding, or some other character code that gives them a more "textbooky" look.

As mentioned above, PEDMAS (or BODMAS, or whatever version of order of operations you prefer) says that exponentiation happens before mutliplication:

P - Parenthesis

E - Exponents

D - Division

M - Multiplication

A - Addition

S- Subtraction

When we see -a, we take that to mean ##-1 \times a##. So ##-3^2## says ##-1 \times 3^2##, so square the three first, then multiply by -1. We aren't pulling anything out of the air:

##-3^2 = -1 \times 3^2 = -1 \times 9 = -9##

-Dan

- #8

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By convention ##-3^2 \equiv -(3^2)##. For example, there is a clear difference (by convention) between these two quadratic expressions:My calculator shows -3² = 9

My calculator also shows 3²=9

Both make sense because -x-=+

-3² should = -3 x -3 = 9

$$-x^2 + bx + c \not\equiv x^2 + bx+c$$This convention is well established, so you ought to learn it.

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- #11

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Right, so you'd forgotten that ##-x^2 \equiv -(x^2)##. That's something you've relearned. Good?I have been out of college 50 years. If you don't use it you loose it. I have forgotten about 90% of what I once knew, maybe more.

- #12

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My calculator shows -3² = 9

Depending on the calculator, it might be that the sequence of keys [3] [-] [x

- #13

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I only know real math symbols, what are ^ & * mean?

They aren't really math symbols, at least they aren't symbols that are commonly used in math textbooks. The caret (^) was first used in BASIC, I believe, to represent exponentiation; i.e., raising a number to some power. Very few other programming languages use ^ for this purpose, however. The asterisk (*) is universally used in programming languages to represent multiplication. Both symbols are commonly used in internet forums to represent these operations.^ and *arereal Math symbols.

- #14

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Just to be clear: If you type ##-3## into your calculator and hit [enter] or '=', then that part is done immediately and the calculator will store -3 somewhere. Then, when you square that, the answer will be ##(-3)^2 = 9##.My calculator shows -3² = 9

That is not the same as ##- 3^2 = - (3^2) = -9##.

A calculator where you can enter a calculation like ##-3^2## in one step, without any intermediate [enter] or '=' should give you the correct answer of ##-9##.

- #15

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Its a free website of over 5000 ten-minute videos walking you thru the steps to solve a problem presented at the start of the video.

It covers the full range of highschool thru first year college math.

- #16

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Right, a negative times a negative is positive, but that's not what you have with ##-3^2##. This means literally, the negative of ##3^2##, not ##(-3) \times (-3)##.Why is +3² different than -3² math rules tell me - x - has to be + and 3 x 3 has to be +9 not -9.

Also "- x -" is a bit confusing. It took me a little while to get that you meant "negative times negative."

- #17

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The original problem is, -3²= ?

There is no way to put parentheses in my calculators. I put -3 in both calculators then push the square button and the answer on both calculators is -3²=9

Everyone adds parentheses to this for some reason claiming it needs parentheses.

I asked the wrong question on this thread. I should have ask what is, -3²= ?

There is no way to put parentheses in my calculators. I put -3 in both calculators then push the square button and the answer on both calculators is -3²=9

Everyone adds parentheses to this for some reason claiming it needs parentheses.

I asked the wrong question on this thread. I should have ask what is, -3²= ?

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- #18

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The standard convention of modern mathematics is that ##-3^2 = -9##. This thread has many explanations of why.I asked the wrong question on this thread. I should have ask what is, -3²= ?

Calculators are not infallible in this respect.

- #19

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##-3^2=-9##The original problem is, -3²= ?

Then you used your calculator wrong. You calculated ##(-3)^2## instead of ##-3^2##.There is no way to put parentheses in my calculators. I put -3 in the calculator then push the square button and the answer on both calculators is -3²=9

To calculate ##-3^2## on your calculator you need to put ##3## in the calculator, then push the square button, and then push the ##-## button which on some calculators may be marked ##\pm##.

If the calculator doesn't have parentheses then it requires you to provide the correct order of operations manually. By entering the ##-## first you incorrectly told the calculator that ##-## had a higher precedence than ##{}^2##. So you told it to calculate ##(-3)^2##

- #20

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4-3^2&=&-5\\

3-3^2&=&-6\\

2-3^2&=&-7\\

1-3^2&=&-8\\

0-3^2&=&-9

\end{eqnarray*}$$Then ask yourself if you'd want ##0-3^2## to be different from ##-3^2##. Should adding a zero make a difference?

- #21

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The only one I know that has no parentheses are HP Reverse Polish Notation calculators. They use RPN style notation which means you input your equations differently than with a TI-83 calculator as an example.

- #22

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Then you will have to do the calculation in two steps in the correct order yourself and not count on the calculator. You will have to calculate ##3^2 = 9## first, and then reverse the sign to get ##-3^2 = -9##.

There is no way to put parentheses in my calculators. I put -3 in both calculators then push the square button and the answer on both calculators is -3²=9

Everyone adds parentheses to this for some reason claiming it needs parentheses.

I asked the wrong question on this thread. I should have ask what is, -3²= ?

If you are going to get into this in a significant way, use the more advanced calculator.

- #23

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I could be wrong, but I seem to recall that some of the cheaper calculators don't have parentheses, but don't use RPN. Also, the Windows calculator, in Standard mode, doesn't have parentheses and doesn't do RPN. To calculate ##-3^2##, you enter 3, click ##x^2##, and then click +/-.The only one I know that has no parentheses are HP Reverse Polish Notation calculators.

If you enter 3, then ##x^2##, then +/-, the result is -9.

- #24

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a*b+c*d*e+ f*g*h ....

There are articles online on how to work without parentheses:

https://study.com/skill/learn/using-the-order-of-operations-without-parentheses-explanation.html

Of course, the WIndows 10 calculator doesn't have parens

and my iPhone simple arithmetic calculator doesn't either (ie in portait mode) However switching to landscape mode and you get a full blown scientific calculator complete with parentheses.

- #25

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If you have been within a metric parsec of Facebook anytime in the last MegaFortnight you have been inundated with PEMDAS riddles like this.

- #26

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## -3^{2}=-9 ## but ## (-3)^2=(-3)(-3)=9 ##.

- #27

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We were checking out a freshman lab, and some students were doing some sort of electrical experiment where they needed to compute the voltage across a 1.5v battery. We asked what voltage they got, and the freshman replied somewhere around 1536v.

We asked: "How did you arrive at that value ?" And the answer we got was that's what the calculator said.

Mic drop.

Time to get back to our senior studies of Quantum Mechanics, the younger generation is hopeless.

- #28

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Yes, that's what we've been saying throughout this thread.## -3^{2}=-9 ## but ## (-3)^2=(-3)(-3)=9 ##.

- #29

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Know your calculatorMy calculator shows -3² = 9

If your enter is something like 'minus, three, square' then (

If your enter is 'three, +/-, square' then it'll take it as a (minus-three) on square

I've seen many cheap (non-decent) ones going with in-order executionThe only one I know that has no parentheses are HP Reverse Polish Notation calculators.

But those rarely had x

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- #30

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We may share how windows10/11 calculator works.

- #31

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My calculator shows -3² = 9

Put your calculator away and try ##-3^2## on your old slide rule.I have been out of college 50 years.

I can't believe this thread has 30 posts. Oops, 31.

- #32

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- #33

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As a historical note…. RPN calculators were developed and brought to market back in the old days when no calculators supported parentheses or understood PEMDAS, which made them far less useful for scientific and technical work. The internal logic of an RPN calculator is appreciably simpler than that of a PEMDAS-aware calculator, which mattered when designing a palm-sized device using 1970s technology.

The only one I know that has no parentheses are HP Reverse Polish Notation calculators. They use RPN style notation which means you input your equations differently than with a TI-83 calculator as an example.

I still prefer the RPN style, as it matches the way we would do the problem unassisted: calculate the highest-precedence intermediate results first and work out the final lowest-precedence step. The ambiguity in ##-3^2## discussed in this thread doesn’t happen in RPN.

- #34

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My take on this as always been:As a historical note…. RPN calculators were developed and brought to market back in the old days when no calculators supported parentheses or understood PEMDAS, which made them far less useful for scientific and technical work. The internal logic of an RPN calculator is appreciably simpler than that of a PEMDAS-aware calculator, which mattered when designing a palm-sized device using 1970s technology.

I still prefer the RPN style, as it matches the way we would do the problem unassisted: calculate the highest-precedence intermediate results first and work out the final lowest-precedence step. The ambiguity in ##-3^2## discussed in this thread doesn’t happen in RPN.

- #35

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The grouping pair symbols show what the boundary is of the expression; even if this expression just a single real number which may also be a signed number.

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