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Math Help - Maths dispute - a very simple simple exponents question

  1. #1
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    Maths dispute - a very simple simple exponents question

    I had an indices test and I got the results back today (I didn't too shabby).

    There was one question though that concerned me.

    It is this one:

    -3^2

    It looks EXACTLY like this. No brackets or anything. Just -3^2

    I wrote  -9 and my teacher marked it wrong. I have asked my friends and they are all divded

    My teacher said it was 9 but I thought i was only 9 when it was (-3)^2

    Who is right?!? :S
    Last edited by jgv115; May 4th 2010 at 01:37 AM.
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  2. #2
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    Quote Originally Posted by jgv115 View Post
    I had an indices test and I got the results back today (I didn't too shabby).

    There was one question though that concerned me.

    It is this one:

    -3^2

    It looks EXACTLY like this. No brackets or anything. Just -3^2

    I wrote  -9 and my teacher marked it wrong. I have asked my friends and they are all divded

    My teacher said it was 9 but I thought i was only 9 when it was (-3)^2

    Who is right?!? :S

    It is my opinion that almost any mathematician, even beginners, will agree that -3^2=-9 as the power does not apply on the minus sign (or, if you prefer, on -1) but only on the immediate expression it is upon.

    Now, it could be that your teacher considers -3 as asingle expression (which, in fact, it is: the additive inverse of 3), but then we have a problem: how could we express the mathematical expression "the additive inverse of (3 raised to the second power)"??
    Should we write the minus sign further away from 3:  -\,\,\,3^2=-9 ?

    These are question I'd ask, very respectfully, my teacher if I were you.

    In general, I'd say you're right.

    Tonio
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  3. #3
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    -3^2 = 9
    Whenever you square a number no matter if its positive or negative the outcome will always be positive. Do it on your calculator. -3*-3 = 9 if it were to be -3*3 then yes it would equal -9. but then the problem wouldn't be -3^2. Just remember whenever you see anything squared the answer will be positive.
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  4. #4
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    -3^2 = -9 ; really means -(3^2)
    (-3)^2 = 9

    That's it, that's all. Roger.
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  5. #5
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    As most have said, -3^2 by convention is -9. But it depends on what convention one decides to use for the “order of operations”. Usually, operations within an expression are evaluated in the following order:

    1. Parentheses (brackets)
    2. Powers (indices, roots)
    3. Multiplication (or division)
    4. Addition (or subtraction)

    The unary minus (additive inverse) follows the rule for multiplication by -1, so it is evaluated after the power has already been evaluated. Some, however, treat the unary minus as an operator whose order of evaluation follows parentheses yet precedes powers. I guess the only way to be sure is to ask your teacher which convention he or she follows.
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