What is the Correct Answer for -2^2?

  • Thread starter gcn_zelda
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In summary, there is a debate about the correct answer for the expression -2^2. Some argue that it is equal to -4, while others argue it is equal to 4. The correct answer depends on where the parentheses are placed, with the standard being that -a^b is equal to -(a^b). Additionally, factoring out numbers and taking them out of parentheses with exponents does not work in the same way as factoring with regular numbers. It is important to follow the correct order of operations to avoid getting incorrect answers.
  • #1
gcn_zelda
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Ever since Algebra, I've been taught that -2^2=4
On another message forum, however there was a debate that -2^2=-4.
They came up with the conclusion that:
-2^2 is the same as -1(2^2) which equals -1(4) equaling -4.
I just wonder what the correct answer is.
 
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  • #2
It depends on your parentheses. Normally, -22 means -(22), which is -4. But if you mean (-2)2, then that is +4.
 
  • #3
Originally posted by gcn_zelda
Ever since Algebra, I've been taught that -2^2=4
On another message forum, however there was a debate that -2^2=-4.
They came up with the conclusion that:
-2^2 is the same as -1(2^2) which equals -1(4) equaling -4.
I just wonder what the correct answer is.

(-2)^2 = 4

and

-(2^2) = -4

are not the same thing.

The correct answer depends on where you put your parentheses.
 
  • #4
2^2 is the same as -1(2^2)
That is an incorrect assumption. You can't just start factoring numbers and taking them out of bracks with exponents, it just doens't work that way. It's hard to put into words so just look at the example.
Lets say I want to square root A^2 + 2AB + B^2. I would write that as (A^2 + 2AB + B^2)^(1/2). The answer to this is (A + B) of course. Now let's say I used the silly logic mentioned above, i factor out an A + B. Now I end up with (A + B)(A + B)^(1/2) which I can't even give an answer for.
Do you see how factoring out completely changes the answer? That is why we never do that.

(-2)^2 = 4
(-2i)^2 = -4

If you want that negative to stay, you need to put an i there :D
 
  • #5
(-2)^2 = (-1)^2*(2)^2 = 1*(2)^2 = 2^2 = 4.

If you take the -1 factor out of -2 you have to raise it to the power of 2 as well.
 
  • #6
Ever since Algebra, I've been taught that -2^2=4
Then, I think, you have been taught wrongly. Or you remember wrongly.

I say:
-22 = -4.

Because convention is: Power has priority over multiplication.

-2 = -1*2.
So,
-22 = -1*22.
Since power has priority, this equals
-1*4 = -4.
 
  • #7
Like Ambitwistor and enigma pointed out, -2^2 is not -1*2^2.

-2 = -1*2
In the next step, squaring both sides results in:
(-2)^2 = (-1*2)^2
In your calculations, you failed to square the -1. While exponents are evaluated before products, paretheses are resolved before exponents. Therefore -1*2 is evaluated first, as -2, which is then squared, resulting in 4.

Another way of evaluating the expression is to apply the exponent to both terms on the right side:
(-1)^2 * (2)^2
Which is equal to:
1 * 4
 
  • #8
Like ambitwistor said, it depends on where you mean the parentheses to be.

However, the standard is that

[tex]
-a^b = -(a^b)
[/tex]

so without any context to indicate otherwise, any mathematician would unambiguously interpret it as above.
 
  • #9
worl sqrt(-9) be 3i or 9i?
 
  • #10
sqrt of (-9):
sqrt of (-9) = sqrt of (9) times the sqrt of (-1)
so sqrt of (9) = 3 and sqrt of (-1) equals i
then sqrt of (-9) = 3i
:)
jk
 

What is the debate surrounding -2^2=-4?

The debate is centered around the order of operations in mathematics and whether the exponent should be applied before or after the negative sign.

What is the general consensus among mathematicians?

The general consensus among mathematicians is that -2^2 does indeed equal -4. This is because the exponent is applied before the negative sign, making it -4 rather than 4.

Why is there confusion surrounding this equation?

There is confusion because some people follow the rule of "PEMDAS" (parentheses, exponents, multiplication, division, addition, subtraction) while others follow the rule of "BODMAS" (brackets, orders, division, multiplication, addition, subtraction). These different rules can lead to different interpretations of the equation.

Is there a correct answer to this debate?

Yes, there is a correct answer. Depending on which rule of order of operations is followed, the answer can be either -4 or 4. However, the general consensus among mathematicians is that the exponent should be applied before the negative sign, making -2^2 equal to -4.

What is the significance of this debate?

The significance of this debate is that it highlights the importance of following a consistent set of rules in mathematics. It also emphasizes the need for clear communication and understanding in mathematical equations.

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