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Negative Number Raised to a Power

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by BlindVision » Mon Mar 23, 2009 3:42 pm
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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by cramya » 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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Typo

by Bhattu » 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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by Ian Stewart » 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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Negative raised to power

by Bhattu » 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
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by BlindVision » 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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by Ian Stewart » 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'.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by cramya » Tue Mar 24, 2009 4:38 pm
Thanks Ian.


Bhattu, I have corrected the typo.

Regards,
CR
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