Help with exponent problem...

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agresj: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Mar 22, 2010 6:27 am

by agresj » Mon Mar 29, 2010 7:36 am

I can't seem to figure out the following problem. I think I'm just blanking on a rule that I should be applying...

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

a) 17
b) 18
c) 34
d) 35
e) 36

Thanks...

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Source: Beat The GMAT — Problem Solving | Mon Mar 29, 2010 7:36 am

arzanr: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Wed Jan 07, 2009 1:56 pm; Thanked: 12 times; GMAT Score:750

by arzanr » Mon Mar 29, 2010 8:00 am

I'm guessing the question is to solve for m?

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

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

[(1/5^m)] * [(1/2^36)] = 1/[(2)^36*(5)^35]

1/[(2)^36*(5)^m] = 1/[(2)^36*(5)^35]

m=35

Let me know if you need help with any of the workings.

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indiantiger: Master | Next Rank: 500 Posts; Posts: 362; Joined: Fri Oct 02, 2009 4:18 amFollowed by: 1 member; Thanked: 26 times

by indiantiger » Mon Mar 29, 2010 9:18 am

Given =

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

lets simplify LHS first

=(1/5)^m * (1/2) ^2*18
=(1/5)^m * (1/2)^36

Now lets simplify RHS
= 1/[2(5*2)^35]
= 1/2*(1/2)^35*(1/5)^35
=(1/2)^36*(1/5)^35

LHS = RHS

(1/5)^m*(1/2)^36 = (1/2)^36 *(1/5)^35

the only way LHS = RHS is for m = 35

(D)

Please feel free to correct me if I have done anything wrong.

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sgarnepudi: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sat Sep 13, 2008 11:30 am

by sgarnepudi » Mon Mar 29, 2010 9:38 am

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

=> 2 *10^35 = 5^m* 4^18

=> [2 *10^35]/ 4^18 = 5^m

=> [2 *10^35]/ 2^36 = 5^m

=> [10^35]/ 2^35 = 5^m

=> [10/ 2]^35 = 5^m

=> 5^35 = 5^m

=> m = 35

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eaakbari: Master | Next Rank: 500 Posts; Posts: 435; Joined: Mon Mar 15, 2010 6:15 amFollowed by: 1 member; Thanked: 32 times

by eaakbari » Mon Mar 29, 2010 10:48 pm

When you do look at the question, you should realize that theres 5 , 4 and 10. 5*2=10. So its preferable to make 4 in terms of two.Lets proceed

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

5^-m * 2^-36 = 1/2 * 10^-35

5^-m * 2^-35 = 10^-35

Which obviously implies m = 35

So D

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