math question (anyone know how to solve)

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LSJK: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Oct 03, 2007 5:27 pm; Thanked: 2 times

by LSJK » Sat Jun 20, 2009 10:15 am

math question (anyone know how to solve):

(1/5)^m * (1/4)^18 = 1/2(10)^35

what does m=?

Answer options:

17, 18, 34, 35, 36

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Source: Beat The GMAT — Problem Solving | Sat Jun 20, 2009 10:15 am

vasbli: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Sat Mar 01, 2008 2:32 pm; Location: Zurich; Thanked: 1 times

by vasbli » Sat Jun 20, 2009 2:03 pm

(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35

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LSJK: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Oct 03, 2007 5:27 pm; Thanked: 2 times

THANK YOU

by LSJK » Sun Jun 21, 2009 1:24 pm

thank you.

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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

by BlindVision » Sun Jun 21, 2009 3:18 pm

vasbli wrote:(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35

Can you please tell me how...
(1/4)^18 became (1/2)^36?

And...

How 1/2(10)^35=1/(2*5^35*2^35) ? Thank you!

Life is a Test

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ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

by ssmiles08 » Sun Jun 21, 2009 3:27 pm

BlindVision wrote:
vasbli wrote:(1/5)^m * (1/4)^18 = 1/2(10)^35
--------
(1/5)^m * (1/4)^18=(1/5)^m * (1/2)^36=(1/5)^m * 1/(2*2^35)
and
1/2(10)^35=1/(2*5^35*2^35)

m=35
Can you please tell me how...
(1/4)^18 became (1/2)^36?

And...

How 1/2(10)^35=1/(2*5^35*2^35) ? Thank you!

BlindVision,

1/4 = (1/2)^2
so [(1/2)^2]^18 = (1/2)^36

and

1/[2*10] = 1/[2*5*2] = 1/[(2*5)*(2)]
since the whole bottom of the fraction is raised to the power of 35, you need to distribute that property to all multiplied products.

= 1/(2*5^35*2^35)

-hope that helps.

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LSJK: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Wed Oct 03, 2007 5:27 pm; Thanked: 2 times

by LSJK » Sun Jun 21, 2009 3:30 pm

Question 1:

4= 2^2

so (2^2)^18= 2^36 because 2 * 18=36

______________________________________
Question 2:

2^2 * 2= 2^3=8

so

2(10)^35 = 2 * 2^35 * 5^35

so based on above. . .

2 * 2^35 = 2^36

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BlindVision: Master | Next Rank: 500 Posts; Posts: 253; Joined: Fri Dec 26, 2008 8:39 pmFollowed by: 1 member; Thanked: 8 times

by BlindVision » Sun Jun 21, 2009 3:41 pm

Aha! I get it! Thank you, SSmiles!

Thanks LSJK, I see your reply in the "post a reply" screen, but not in the regular screen.

Life is a Test

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