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If x = 4, then

If x = 4, then Image
(A)    –14
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set S: Exponents & Roots

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Posted: 08/10/2012 16:24
Isn't this answer wrong. -I've number when raised to even power is always positive? Ans should be 18
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Posted: 08/10/2012 16:32
Saurabh, recall that power operation happens first before negation (which is simply multiplication by -1. Hence -2^2 is 4. (-2)^2 is 4.
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Posted: 10/30/2012 23:32
I'm still confused. -2^4 equals 16, correct? Then the answer should be E=18. Why would a negative raised to the power of 4 stay negative? Thanks for clarifying.
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Posted: 10/31/2012 02:45
Mona, recall that power operation happens first before negation (which is simply multiplication by -1. Hence -2^4 is -16. (-2)^4 is 16.
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Posted: 12/03/2012 01:00
Is it that only if there is a bracket should we consider the rule that a negative number raised to a positive no is positive?
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Posted: 12/03/2012 03:59
Vaishnavi,
Negative numbers raised to odd powers stay negative
Negative numbers raised to even powers become positive
Regardless of the leading power sign.

Niels

PS.
Joel I'm not in your hair, how could I? :)
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Posted: 12/03/2012 01:50
Vaishnavi, the answer is yes. It's about the order of operation: PEMDAS (parentheses or brackets, exponent, multiplication/division, addition/subtraction)
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If x = 4, then 
Posted: 01/27/2014 20:30
Even if you do exponent first you still get -2^4 = (-2)(-2)(-2)(-2)= 16. Regardless if it's preceded by -1. (-1)(2)(-1)(2)(-1)(2)(-1)(2)=16 +2=18. Had it be. -(2)^4 then I would believe the answer to be -14.
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Posted: 01/27/2014 21:50
Marvin, you raise 2, not -2, to the 4th power, then multiply by -1. So it's exponent first then multiplication (pEMda)
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Posted: 01/28/2014 05:23
Ok? When i enter this equation on my calculator I get 18. Why doesn't it show -16?
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Posted: 01/28/2014 07:50
Marvin, maybe there's something wrong with your calculator or the way it is set up. Enter -2^4 into Google search bar and see what happens :)

You can either hang on to your belief and calculator, or trust Google and the explanations here about the order of math operations. Google Chrome even put in the parentheses in the right places in the calculator in order to show the intermediate step.
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Posted: 01/28/2014 06:59
Marvin,

Like Joel describes in his reply from 10/31/2012 02:45

-3^3 = should be read as (-1)(3)^3 = (-1)(3*3*3) = -9
(-3)^3 = should be read as is and becomes (-3)*(-3)*(-3) = -9
And from there the rule applies negative number to odd power remains negative and a negative number to an even power becomes positive.

Hope this helps.
Niels
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If x = 4, then 
Posted: 11/14/2014 16:44
Niels makes a great point, but I'd like to know why we 'should' read -2^4 as -1(2^4) and not (-1*2)^4. I'll definitely do PEMDAS if the parents are there. In this case, the operation is hidden and I never learned a rationale for the default used here.
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Posted: 11/15/2014 03:50
Hi Neil,

This issue is somewhat contrived and very subtle and therefore should not be presented on the test. Nevertheless and surprisingly, the GRE does test this issue.

Now, -2 can be interpreted as -1 x 2. In this form, it is clear that the exponent does not apply to the negative one: -2^4 = -1 x 2^4 = -1 x 16 = -16.

However, this interpretation is subject to the following criticism:

Although -2 can be written as -1 x 2, this is not its definition. It is an inviolate number (unaltered, intact), just as distinct as the number 2.

With this interpretation, -2^4 = (-2)^4 =(-2)(-2)(-2)(-2) = +16.

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