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Fractions and Powers

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Fractions and Powers [#permalink] New post 22 Dec 2009, 15:58
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91% (02:35) correct 8% (01:56) wrong based on 1 sessions
Hi everyone,
I did the GMATPrep exam yesterday and here was my first question. Kind of threw me off :oops: . Any thoughts?
(\frac{1}{5})^m (\frac{1}{4})^{18} = \frac{1}{2(10)^m}

m=
a.17
b.18
c.34
d.35
e.36

[Reveal] Spoiler:
D. 35
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 19:18
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split the 10 into 5^m * 2^m

(1/5)^m * (1/4)^18 = 1/2 * (1/5^m *1/2^m)

1/5^m cancels on both sides

and (1/4)^18 can be written as (1/2)^36

so
(1/2)^36 = 1/2 * 1/2^m

1/2^35 = 1/2^m

M = 35

does this help you... ?
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 20:31
M=35
Split the right side
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A kudos would greatly help :)

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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 20:49
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brentbrent wrote:
Hi everyone,
I did the GMATPrep exam yesterday and here was my first question. Kind of threw me off :oops: . Any thoughts?
(\frac{1}{5})^m (\frac{1}{4})^{18} = \frac{1}{2(10)^m}

m=
a.17
b.18
c.34
d.35
e.36

[Reveal] Spoiler:
D. 35


(\frac{2*2^m *5^m}{5^m})= 2^{2*18}

2^{m+1}=2^{36}

m+1=36

m=35
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 21:34
*...is seen smacking palm on face* :roll:

thanks guys.
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 21:39
[(1/5)^m]*[1/4]^18=[(1/2)*(1/10^m)]

(1/5)^m * (1/2)^36 - [ (1/2)*(1/2^m)*(1/5^m)]=0
(1/5)^m[(1/2)^36-(1/2)^m+1]=0
(1/2)^36=(1/2)^m+1
---->m+1=36
m=35
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Re: Fractions and Powers   [#permalink] 22 Dec 2009, 21:39
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