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Fractions and Powers

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Fractions and Powers [#permalink] New post 22 Dec 2009, 14:58
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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, 18:18
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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... ?
Manager
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 19:31
M=35
Split the right side
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A kudos would greatly help :)

Tuhin

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Posts: 115
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Schools: IU KSB
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 19:49
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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


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

\(2^{m+1}=2^{36}\)

\(m+1=36\)

\(m=35\)
Intern
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Joined: 29 Nov 2009
Posts: 22
Location: Toronto
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Kudos [?]: 8 [0], given: 5

Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 20:34
*...is seen smacking palm on face* :roll:

thanks guys.
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Posts: 202
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Re: Fractions and Powers [#permalink] New post 22 Dec 2009, 20:39
[(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, 20:39
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