Algebra with negative exponents

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700goal: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Mon Nov 24, 2008 12:14 pm

by 700goal » Mon Nov 24, 2008 12:32 pm

I ran into this question on one of the GMAT prep CATs and I don't really know how to attack it. Thanks,

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

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Source: Beat The GMAT — Problem Solving | Mon Nov 24, 2008 12:32 pm

mals24: Legendary Member; Posts: 683; Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members; Location: Dubai; Thanked: 73 times

by mals24 » Mon Nov 24, 2008 2:47 pm

(1/4)^18 can be written as (1/2)^36 [4^18 = [(2)^2]^18 = 2^(18*2)]

(1/2)^36*(1/5)^m = 1/[2*(10)^35]

2*(10)^35 = 2*(2^35*5^35) = 2^36*5^35

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

1/2^36 will get canceled from both sides.

(1/5)^m = (1/5)^35

5^35 = 5^m

m = 35

You just have to apply the exponent rules here.

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awilhelm: Master | Next Rank: 500 Posts; Posts: 117; Joined: Fri Oct 17, 2008 7:41 am

another path?

by awilhelm » Fri Jan 16, 2009 10:39 pm

Is it possible to solve this problem by beginning in the following way?

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

4^-18 * 5^-m = 5^35

what would be the next step?

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DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Sat Jan 17, 2009 12:51 am

You could maybe find the answer a bit faster if you just dropped the "1/". Because what you have there is equivalent to:
4^18*5^m=2*(10)^35
4=2^2 and 10 = 2*5, so you get 2^36*5^m=2*2^35*5^35=2^36*5^35, so m=35.

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