GMAT Prep ?? (Roots)

[dferm]

Please Help...

I know it is simple but these questions seem to be taking me a lot of time...

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

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

Please explain a concise way of applying methods to these kinds of problems.

Thanks.

[pepeprepa]

You are right you must not spend time on this type of question.

(1/5)^m (1/4)^18 = 1/(2*(10)^35)
(I hope this is how the question starts, I am not sure given how the parenthesis are placed)

Let's try to put the right part of the equation in the same organization as the left part, I mean with 1/5 and 1/4

1/(2*(10)^35)= 1/2 * 1/(10^35)
you know 10=5*2 so we can write
1/(2*(10)^35)= 1/2 * 1/(5^35 * 2^35)
1/(2*(10)^35)= 1/(2^36) * 1/5^35
2^36=2^(18*2)=(2^2)^18=4^18 so we can write:
1/(2*(10)^35)= 1/( 4^18 ) * 1/5^35

Now let's compare it to the left part:

(1/5)^m * (1/4)^18= 1/( 4^18 ) * 1/5^35

You have your answer.
For this kind of question you must now common rules on powers, and you have to try to compare both sides so to put them with the same factors.

[leugene]

What a brilliant explanation. Thanks.

[4meonly]

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

thanx to pepeprepa for
(1/5)^m (1/4)^18 = 1/(2*(10)^35)


Yesterday I was stuck with the 1st one...