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Negative Number Raised to a Power

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BlindVision Really wants to Beat The GMAT!
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Negative Number Raised to a Power Post Mon Mar 23, 2009 3:42 pm
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    Can someone refresh me on a rule or illustrate the logic that a negative number raised to any power still yields a negative answer?

    examples:

    -2^2 = -4

    -2^5 = -32

    -3^2 = -9

    -3^3 = -27

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    cramya GMAT Titan Default Avatar
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    Post Mon Mar 23, 2009 3:59 pm
    (negative integer) raised to (even positive power) is positive.


    (-2) ^ 2 = 4 (not -4 as stated above)

    (-2) ^ 4 = 16

    (negative integer) raised to (odd positive power) is negative

    (-2)^3 = -8
    (-2)^1 = -2

    Hope this helps.



    Last edited by cramya on Tue Mar 24, 2009 4:38 pm; edited 2 times in total

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    Bhattu Just gettin' started! Default Avatar
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    Post Tue Mar 24, 2009 1:00 am
    cramya wrote:
    (negative integer) raised to (even positive power) is positive.


    -2 ^ 2 = 4 (not -4 as stated above)

    -2 ^ 4 = 16

    (negative integer) raised to (odd positive power) is positive.

    -2^3 = -8
    -2^1 = -2

    Hope this helps.
    I think there was a typo, shouldn't it be = (negative integer) raised to (odd positive power) is negative?

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    Ian Stewart GMAT Instructor
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    Post Tue Mar 24, 2009 8:28 am
    cramya wrote:
    (negative integer) raised to (even positive power) is positive.

    -2 ^ 2 = 4 (not -4 as stated above)
    Here, it really depends on how the expression is written. If you raise -2 to the power of 2, the answer is certainly positive 4. That is, if you have:

    (-2)^2

    that is equal to 4, because this is equal to (-2)*(-2). However, if the negative is not enclosed in brackets, as was written in the original post:

    -2^2

    then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

    -2^2 = -4

    because this is equal to -(2)*(2).

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    Bhattu Just gettin' started! Default Avatar
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    Post Tue Mar 24, 2009 9:11 am
    Thanks for that - helps clarify that for me and also probably a careless error I should be aware of

    BlindVision Really wants to Beat The GMAT!
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    Post Tue Mar 24, 2009 9:23 am
    Ian Stewart wrote:
    then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

    -2^2 = -4

    because this is equal to -(2)*(2).
    What does the "B" in "BEDMAS" stand for? "Brackets"? Thank you!

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    Ian Stewart GMAT Instructor
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    Post Tue Mar 24, 2009 10:12 am
    BlindVision wrote:
    Ian Stewart wrote:
    then by order of operations (BEDMAS), we must raise 2 to the power 2 first, then take the negative of that. So, if there are no brackets,

    -2^2 = -4

    because this is equal to -(2)*(2).
    What does the "B" in "BEDMAS" stand for? "Brackets"? Thank you!
    Yes, 'brackets'. The mnemonic is sometimes presented as 'PEDMAS', where the P stands for 'parentheses'.

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    Post Tue Mar 24, 2009 4:38 pm
    Thanks Ian.


    Bhattu, I have corrected the typo.

    Regards,
    CR

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