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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Algebra with negative exponents
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mals24
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(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.
(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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DanaJ
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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.
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.
