Fractions and Powers : PS Archive
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# Fractions and Powers

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Intern
Joined: 29 Nov 2009
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Location: Toronto
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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 . 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
Intern
Joined: 13 Dec 2009
Posts: 11
Followers: 0

Kudos [?]: 4 [2] , given: 7

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22 Dec 2009, 18:18
2
KUDOS
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

Manager
Joined: 23 Nov 2009
Posts: 53
Followers: 1

Kudos [?]: 11 [0], given: 1

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22 Dec 2009, 19:31
M=35
Split the right side
_________________

A kudos would greatly help

Tuhin

Manager
Joined: 13 Oct 2009
Posts: 115
Location: USA
Schools: IU KSB
Followers: 4

Kudos [?]: 80 [1] , given: 66

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22 Dec 2009, 19:49
1
KUDOS
brentbrent wrote:
Hi everyone,
I did the GMATPrep exam yesterday and here was my first question. Kind of threw me off . 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
Joined: 29 Nov 2009
Posts: 22
Location: Toronto
Followers: 0

Kudos [?]: 16 [0], given: 5

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22 Dec 2009, 20:34
*...is seen smacking palm on face*

thanks guys.
Manager
Joined: 09 May 2009
Posts: 203
Followers: 1

Kudos [?]: 218 [0], given: 13

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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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