Powers and Roots - GMAT Prep question

[acaba007]

I got this question on my test, and I cant figure out why the correct answer is D:

If (1/5)^m * (1/4)^18 = 1/2(10)^35, then m = ?
a. 17
b. 18
c. 34
d. 35
e. 36

Can someone please explain why?

[aimscore]

hi,

There is a typo in the question.

https://www.beatthegmat.com/gmatprep-exp ... t8855.html

Heres how I solved it.

(1/5)^m * (1/4)^18 = (1/2) *(1/10)^35
(1/5)^m * (1/2 *1/2)^18 = (1/2) * [(1/5 *1/2)]^35
(1/5)^m * (1/2)^18 * (1/2)^18 = (1/2) * (1/2)^35 * (1/5)^35
(1/5)^m * (1/2)^36 = (1/2)^36 * (1/5)^35

Cancelling (1/2)^36 on both sides we get,

(1/5)^m = (1/5)^35
Hence m =35
Ans : D
Hope this helps..