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Exponents and Fractions!

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Source: — Problem Solving |

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by Brent@GMATPrepNow » Sun Jul 07, 2013 3:16 pm
chandlerburton wrote:If (1/5)^m * (1/4)^18 = = 1 / 2(10)^35 , then m =
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GMAT/MBA Expert

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by Brent@GMATPrepNow » Sun Jul 07, 2013 3:54 pm
chandlerburton wrote:If (1/5)^m * (1/4)^18 = = 1 / 2(10)^35 , then m =

Thanks!
An even faster approach is to focus solely on the 5's.
(1/5)^m * (1/4)^18 = 1/2(10)^35 [original equation]
(1/5)^m * (1/4)^18 = 1/2(2 * 5)^35 [rewrote 10 as 2 * 5]
(1/5)^m * (1/4)^18 = 1/[2(2^35) * (5^35)] [applied power of a product rule]
(1/5)^m * (1/4)^18 = 1/(2^36) * 1/(5^35) [rewrote right-hand side]
(1/5)^m * (1/4)^18 = 1/(2^36) * (1/5)^35 [rewrote 1/(5^35)]
(1/5)^m * (some stuff with 4's) = (some stuff with 2's) * (1/5)^35 [ignore non-5 stuff]

m = 35

Cheers,
Brent
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by chandlerburton » Mon Jul 08, 2013 5:53 am
Excellent, thank you!
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