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Exponents

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by heshamelaziry » Mon Sep 21, 2009 3:33 pm
The value of (2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is how many times the value of 2^-17 ?

The answer seems to have a flaw in multiplying fractions !!!
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Re: Exponents

by Brent@GMATPrepNow » Mon Sep 21, 2009 6:00 pm
heshamelaziry wrote:The value of (2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is how many times the value of 2^-17 ?

The answer seems to have a flaw in multiplying fractions !!!
For some reason, I'm having a hard time adding an image to the post. So, I've attached the solution.

Cheers,
Brent
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Re: Exponents

by heshamelaziry » Mon Sep 21, 2009 6:11 pm
Brent Hanneson wrote:
heshamelaziry wrote:The value of (2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is how many times the value of 2^-17 ?

The answer seems to have a flaw in multiplying fractions !!!
For some reason, I'm having a hard time adding an image to the post. So, I've attached the solution.

Cheers,
Brent
it shuold be ((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 )/ 2^-17 which translates to:

((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 * 1/ 2^-17.

I don't know what i am missing ! i.e (2/5)/4 = 2/5 * 1/4. Shouldn't it be the same principal ?
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Re: Exponents

by Brent@GMATPrepNow » Mon Sep 21, 2009 6:19 pm
heshamelaziry wrote:
Brent Hanneson wrote:
heshamelaziry wrote:The value of (2^-14 + 2^-15 + 2^-16 + 2^-17)/5 is how many times the value of 2^-17 ?

The answer seems to have a flaw in multiplying fractions !!!
For some reason, I'm having a hard time adding an image to the post. So, I've attached the solution.

Cheers,
Brent
it shuold be ((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 )/ 2^-17 which translates to:

((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 * 1/ 2^-17.

I don't know what i am missing ! i.e (2/5)/4 = 2/5 * 1/4. Shouldn't it be the same principal ?
It's probably easier to rewrite ((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 )/ 2^-17 as ((2^-14 + 2^-15 + 2^-16 + 2^-17)/5 ) x 2^17

Then you get: (2^3 + 2^2 + 2^1 + 1)/5 = 3

Useful rule here: 1/(x^-n) = x^n
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