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 Post subject: GMAT Algebra
PostPosted: Tue Feb 22, 2011 4:44 pm 
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Joined: Sun May 30, 2010 3:15 am
Posts: 424
If (1/4)ª × 2³ = (1/2)³ª then a =

A. -3
B. -2
C. 0
D. 3
E. 4

(A) (1/4)ª × 2³ = 2 to the (3 – 2a)-th power.
(1/2)³ª = 2 to the (-3a)-th power.

Equality holds if powers are equal.
3 – 2a = -3a
a = -3
The correct answer is choice (A).
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I don't understand how we are able to get the powers to have like numbers below them here. I understand that if your are able to get the variables or number the same then you can just set the powers equal but don't know how to come up with ther here. Thank you.


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 Post subject: Re: GMAT Algebra
PostPosted: Tue Feb 22, 2011 5:02 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
(1/4)ª × 2³ = (1/2)³ª

We're looking for the same base, 2.
Using properties of exponents, we can see that current bases are powers of 2:
Image

Then we can plug in the simplified terms and use properties of exponents to arrive to the final equation form:
Image

If these transformations are NOT clear to you, you should go over the properties of exponents:
http://www.800score.com/gmat-guide.html


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 Post subject: Re: GMAT Algebra
PostPosted: Thu Jul 07, 2011 4:49 pm 
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Posts: 424
How do you get this answer?
Why does (1/4)ª × 2³ = 2 in (3 – 2a)-th power?


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 Post subject: Re: GMAT Algebra
PostPosted: Thu Jul 07, 2011 5:01 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
Take a look at the explanation above. What we do there is we use the regular properties of exponents. Take a look of how we convert (1/4)ª into 2 in the (-2a)-th power.

If something in it is unclear to you, go over the properties of exponents and try to see which ones we apply here. If you have any questions left then, fell free to ask (specifying which exact step is unclear).


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