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Exponent Problem

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by gator85 » Sun Feb 15, 2009 6:01 am
I was taking a practice test from the GMAT software and this PS question stumped me:

5^21 x 4^11 = 2 x 10^n
what is n=?

I don't have the answer choices handy. But my thought was there's no way GMAT wants me to solve this by hand. Am I missing a trick?

Please Help!!! Thanks!!
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by dendude » Sun Feb 15, 2009 6:18 am
n is 21

(5^21)*(4^11) can be written as
(5^21)*((2^2)^11) = (5^21)*(2^22)
= 2*(5*2)^21
=2*10^21
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by ManuGMAT » Sun Feb 15, 2009 7:20 am
5^21 * 4^11 = 2 * 10^n
=2 * (2*5)^n = 2 * 2^n * 5^n = 2^(n+1) * 5^n = 4^(n+1)/2 * 5^n

so, n=21
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