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francoisph: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 07, 2010 3:15 pm; Thanked: 1 times

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by francoisph » Fri Jun 04, 2010 4:44 am

Hi,

could you resolve below?

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

thks

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Source: Beat The GMAT — Problem Solving | Fri Jun 04, 2010 4:44 am

papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pm; Thanked: 653 times; Followed by:252 members

by papgust » Fri Jun 04, 2010 6:32 am

I searched the forum with keyword "(1/5)^m". And i got so many links. To name a few,

https://www.beatthegmat.com/1-5-m-1-4-10 ... 56166.html
https://www.beatthegmat.com/gmatprep-exp ... t8855.html

Please do search for a question next time before you post. Thank you!

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Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pm; Location: New York City; Thanked: 76 times; Followed by:17 members; GMAT Score:770

by Rich@VeritasPrep » Fri Jun 04, 2010 6:36 am

Hi there,

Just to clarify what you're posting, I'm taking what you wrote to mean the following:

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

If that's the case, then here's the approach:

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

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

At this point, you can actually stop, because you'll notice that on the right side of the equation, 5^35 is the only term involving a base of 5. The left side of the equation has only one term involving base 5, so we can conclude that the two base 5 terms must have the same exponent.

Final answer: [spoiler]m = 35[/spoiler]

Rich Zwelling
GMAT Instructor, Veritas Prep