You can convert that equation into:

5^m 2^36 = 2 (2x5)^35

5^m 2^36 = 2 2^35 5^35

so: 5^m = 5 ^35 ; therefore m=35

Just got back to the GMAT fray after a 2 month break.

Thought of adding some explanation to Logitech's solution.
Hope he doesnt mind

Every term in this equation is in the denominator. So taking the reciprocal will not alter it in anyway.
here are the steps:

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

Taking reciprocal on both sides:
5^m * 2^36 = 2^36 *5^35
cancelling 2^36,

5^m = 5^35.

Bases are same, so powers can be equated.

m =35

HT Helps

vittalgmat wrote:Just got back to the GMAT fray after a 2 month break.

Welcome back Vittal!

Thank you so much