Fraction to a negative exponent :: Manhattan GMAT Forums

Posted: Thu Aug 02, 2007 5:40 pm

Hi,
When you raise a fraction to a negative exponent, does that always equal a positive whole number? Please explain why or why not.
Thanks

Posted: Thu Aug 02, 2007 7:24 pm

mrkamal,

The result will depend on the fraction itself. If the fraction is +ve then the result will be +ve, if the fraction is -ve then the result will be -ve too. Here is an example: -

(1/2)^-3 = 1/(1/2)^3 = 8 (+ve)

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

Hope it helps

GMAT 2007

Posted: Thu Aug 02, 2007 8:55 pm

Yes, that's very clear.
Thanks a lot!

Posted: Thu Aug 02, 2007 11:37 pm

Good explanation!

Posted: Fri Aug 03, 2007 9:21 am

GMAT 2007 wrote:

mrkamal,

The result will depend on the fraction itself. If the fraction is +ve then the result will be +ve, if the fraction is -ve then the result will be -ve too. Here is an example: -

(1/2)^-3 = 1/(1/2)^3 = 8 (+ve)

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

Hope it helps

GMAT 2007

(-1/2)^-4 = 1/(-1/2)^4 = 8 (+ve)

FOr a positive fraction, its always positive. For a negative fraction, it depends on the exponent.

Posted: Fri Aug 03, 2007 9:32 am

Good point givemeanid. I thought about that too after posting. :) So in all it won't be a positive whole number all the time. But it will depend on the sign of exponential.

GMAT 2007

Posted: Fri Aug 03, 2007 9:45 am

"+ve" - I've seen this term used a fair number of times. I must be unitiated - can someone please tell me what this means. same goes for "-ve".

Thanks!

Posted: Tue Aug 07, 2007 1:08 pm

those are shorthand for positive and negative :)