I need help with a math problem..please don't laugh

The right hand side should be 1/(2 * 10^35).

(1/5)^m * (1/4)^18 = 1/(2 * 10^35)
Breakout the terms in the right hand side (1/5)^m * (1/4)^18 = 1/2 * (1/10)^35
Breakout the terms to their prime factors (4 on the left side and 10 on the right): (1/5)^m * (1/(2^2))^18 = 1/2 * [(1/5)*(1/2)]^35
(1/5)^m * (1/2)^(2*18) = 1/2 * (1/5)^35 * (1/2)^35 --> (1/5)^m * (1/2)^36 = (1/2) * (1/5)^35 * (1/2)^35
Combine the (1/2) in the right hand side: (1/5)^m * (1/2)^36 = (1/5)^35 * (1/2)^36
Solving for m gives you 35. Choice D.

Hi
Are you sure about the "2" in the expression? is it correct?

According to the rules for this kind of problem, you should do the following:

First: Try to factor any sums that may exist in the expression, turning them into multiplications (in this case this is not a problem as there are no sums).

Second: Factor every number into their primes. This is the key to solve this problem:
(1/5)^m (1/4)^18 = 2(1/10)^35 =
(1/5)^m (1/2) ^18 (1/2) ^18 = 2(1/2)^35 (1/5)^35

Third: Cancel out all factors and simplify the expression:
(1/5)^m (1/2) ^36 = 2(1/2)(1/2)^34 (1/5)^35 =
(1/5)^m (1/2) ^36 = 2(1/2)(1/2)^34 (1/5)^35 =
(1/5)^m (1/2) ^2 = (1/5)^35

The problem here is that you get (1/2) ^2 in the end, which you can't cancel. If the expressionis correct, does anyone has any ideas?

November Rain,

Yes the placement of the number 2 is correct; that is one of the primary pieces of the problem that really confused me.

I edited my response to keep the notation the same as the answer given. This question is from zuleron's 198 700+ questions (question 1), and there is a typo in the right hand side.

mp2437,

Thank you very much for the help. I will edit the question on the right handside so it is correct.

What's also interesting, is this question was the first question on the GMATPrep Software, which I downloaded from mba.com!

Thanks again.

answer is D- 35

these type of questions frequently appear on gmat.I have got similar 1st questions on actual GMAT and alos on gmat prep.

Is this correct ?

5^-m * 2^-36 = 1/ 2^36 * 5^35

5^-m * 2^-36 = 2^-36 * 5^-35

-m = -35 ----> m = 35


I am not sure if mp2437 solution was necessarily long ?