Fractions and Exponents.

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carllecat
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Topic: Fractions and Exponents.
PostTue Nov 17, 2009 9:07 am
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If (1/5)^m (1/4)^18 = 1/2(10)^35, then m=

A) 17
B) 18
C) 34
D) 35
E) 36

Answer to be posted later.
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carllecat
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PostTue Nov 17, 2009 9:39 am
D) 35
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carllecat
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PostWed Nov 18, 2009 8:21 am
Anyone???
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Ian Stewart
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PostWed Nov 18, 2009 8:34 am
carllecat wrote:
If (1/5)^m (1/4)^18 = 1/2(10)^35, then m=

A) 17
B) 18
C) 34
D) 35
E) 36

Answer to be posted later.
You can prime factorize, and use exponent rules:

* The left side of the equation is equal to (1/5^m)*(1/(2^2)^18) = 1/[5^m * 2^36]
* The right side of the equation is equal to 1/[(2)*(2*5)^35] = 1/[ (2^1) * (2^35 * 5^35) ] = 1/[ 2^36 * 5^35]

The left and right sides are equal, so we have:

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

Now cross multiply, or take reciprocals on both sides, and cancel the 2^36 to find:

5^m = 5^35
m = 35
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carllecat
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PostWed Nov 18, 2009 9:15 am
Thanks Ian, easy to understand.

Cheers.
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