Beat The GMAT a GMAT & MBA community

Hey, how's it going? Welcome the the Beat the GMAT community. If you have not done so, you should definitely try searching this question since it has probably been posted often. However, I will provide a solution.

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

Notice that 1/(2(10^35)) = 1/(2*(2*5)^35)) = 1/(2*(2^35)*(5^35)) = 1/(2^36*5^35)

Also, note that (1/4)^18 = (1/(2^2))^18 = 1/(2^36)

So we have:

(1/5)^m x 1/(2^36) = 1/(2^36) x 1/(5^35)

From comparing both sides, looks like m = 35.

Hope that helps!

Remember some of your exponent properties for this problem:
(x^a)^b = x^(ab)
(x/y)^a = (x^a)/(y^a)

That is awesome! Thank you!

Some of those properties of exponents questions have been killing me.