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Algebra with negative exponents

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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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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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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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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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