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I need help with a complicated power problem

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by Matt@VeritasPrep » Thu Aug 08, 2013 7:39 am
I usually start by factoring out the smallest power of the common base that's been added (click the image, for some reason it got cut down):

Image

From here, divide both sides by 3^(-8), and you're left with (1+3+9+27)/4 = x, or x = 10.

This works on all sorts of factoring problems on the GMAT, so it's a great technique.
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by GMATGuruNY » Thu Aug 08, 2013 7:42 am
If (3ˉ� + 3ˉ� + 3ˉ� + 3ˉ�)/4 = x * 3ˉ�, what is the value of x?
Strategy: Factor out the MOST NEGATIVE EXPONENT.

Factor out 3ˉ�:
3ˉ� (1 + 3 + 3² + 3³) / 4 = x * 3ˉ�

Cancel out 3ˉ� and simplify:
(1 + 3 + 9 + 27)/4 = x

40/4 = x

10 = x.
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by STI-R » Thu Aug 08, 2013 4:35 pm
Thank you guys for the help!
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