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Please Help!

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Junior | Next Rank: 30 Posts
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by Kobe_Kassidy » Mon Aug 06, 2012 8:10 am
New Member here. This place looks amazing!

Here's my problem

If (1/5)^m X (1/4)^18 = 1/2(10)^35, what is m?

I apologize I don't have all the answer choices. All I know is that the answer is m = 35

How do you get this answer?
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Source: — Quantitative Reasoning |
Master | Next Rank: 500 Posts
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by truplayer256 » Mon Aug 06, 2012 10:49 am
Hey, how's it going? Welcome the the Beat the GMAT community. If you have not done so, you should definitely try searching this question since it has probably been posted often. However, I will provide a solution.

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

Notice that 1/(2(10^35)) = 1/(2*(2*5)^35)) = 1/(2*(2^35)*(5^35)) = 1/(2^36*5^35)

Also, note that (1/4)^18 = (1/(2^2))^18 = 1/(2^36)

So we have:

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

From comparing both sides, looks like m = 35.

Hope that helps!

Remember some of your exponent properties for this problem:
(x^a)^b = x^(ab)
(x/y)^a = (x^a)/(y^a)
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Junior | Next Rank: 30 Posts
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by Kobe_Kassidy » Mon Aug 06, 2012 11:43 am
That is awesome! Thank you!

Some of those properties of exponents questions have been killing me.
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