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

[GMAT 5/18]

Hi everyone,

Could someone please help me solve this question? Thank you!

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

a. 17
b. 18
c. 34
d. 35
e. 36

[dbernst]

No problem!

(1/5)^m = 1/5^m, and (1/4)^18 = 1/4^18 (since 1 raised to any power = 1)
Additionally, 4^18 = (2^2)^18 = 2^36.

Since both sides of the equation have 1 in the their numerators, to set them = we have to set the demoninators equal to each other.

The denominator of the left side is now = 5^m*2^36

The denominator of the right side = 2(10)^35, which can be rewritten as (2)(2*5)^35, or (2)(2^35)(5^35).
Since (2)(2^35)= 2^36, 2^36 can be cancelled from each side of the equation. We are now left with 5^m = 5^35. m = 35, and the correct answer is D

[GMAT 5/18]

Hey Dan,

Thanks heaps! It seems so easy when someone else does it!

This was my very first question when I took the mba.com GMATPrep test, so I assume the GMAC considers this to be approx. a 500 level question - seems more difficult than a 500 level question to me, but perhaps it isn't.

Anyways, thanks again!

[Stinam81]

Could we also solve this by setting the numbers equal to a negative exponent and solving? My first inclination when I saw this problem was to change (1/5)^m to 5^-m, etc., for all numbers. But I had trouble solving that way.

[tim]

this sounds like a viable approach. keep working at this and see if you can make some more progress..