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

Another approach is to focus solely on the 5's.
(1/5)^m * (1/4)^18 = 1/2(10)^35 [original equation]
(1/5)^m * (1/4)^18 = 1/2(2 * 5)^35 [rewrote 10 as 2 * 5]
(1/5)^m * (1/4)^18 = 1/[2(2^35) * (5^35)] [applied power of a product rule]
(1/5)^m * (1/4)^18 = 1/(2^36) * 1/(5^35) [rewrote right-hand side]
(1/5)^m * (1/4)^18 = 1/(2^36) * (1/5)^35 [rewrote 1/(5^35)]
(1/5)^m * (some stuff with 4's) = (some stuff with 2's) * (1/5)^35 [ignore non-5 stuff]

m = 35

Cheers,
Brent

Hi AZ2hot,

The explanations/information provided by the people who commented in this post are correct (and exactly what you need to know).

In answer to your last question though...

No, this question is not too hard for the first question. This is a mid-level prompt, it has just 1 variable and the question itself is based on a few public-domain exponent rules that you were probably taught when you were 14 years old. If you're a little "rusty" on the rules, then that's understandable. Most people don't use exponent rules in their day-to-day lives, so this question might seem harder than it actually is. Once you know the rules though, it's straight-forward enough.

A big takeaway from this question is that you might need to brush up on the various math formulas and rules that the GMAT will present to you, so that you're ready the next time an exponent rule question shows up.

GMAT assassins aren't born, they're made,
Rich