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

[w103mjkkanemj]

I have no idea how to solve the problem below, any help would be greatly appreciated. Thanks.

(1/5)^m (1/4)^18 = 1/(2 * 10^35), what is the value of m?

A. 17

B. 18

C. 34

D. 35

E. 36

[mp2437]

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.

[November Rain]

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?

[w103mjkkanemj]

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.

[mp2437]

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.

[w103mjkkanemj]

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.

[munaf]

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.

[heshamelaziry]

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 ?