Difficult Quant - Exponent Question

GMATpaduan wrote:Any idea on how to get the solution to the following problem?

(1/5)^m * (1/4)^18 = 1/2(10)^35 - what is m?

(1/5)^m * (1/4)^18
= (1/5)^m * (1/2)^36
= (1/5)^m*(1/2)^m*(1/2)^36-m
= (1/10)^m*(1/2)^36-m

We can either use 36-m = 1, which gives us m =35 (co-efficients of 2)
or use co-efficients of 1/10 which gives us 35 directly

Thank you. That is helpful.

Your way led me to a very similar way to work it out, without using the algebra: Is this method also valid?

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

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

(1/5)^m * (1/2)^1 * (1/2)^35 = (1/2^35) * 1/10^35)

(1/10)^m * (1/2)^35 = (1/2^35) * 1/10^35)

m = 35

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

Is this truly the correct formula? Or is the right side of the equation supposed to be 1/2*(1/10)^35?

In your math steps, as shown below, you go from 1/2*(10)^35 to (1/2)^35*(1/10)^35, but those are simply not equivalent.

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

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

If the problem statement is exactly as you've written it, then you should come to this:

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

Hence, the equation doesn't make sense unless the right side is (1/10)^35.

Can someone verify? This seems obvious to me, but maybe I'm missing something.

Thanks!

I was wondering that very same thing. These questions in general usually pose a challenge for me so maybe Im missing something too.