some help pl-how to approach this Question

[gettin there]

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

[logitech]

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

Approach in the dark, when it is less expecting you

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

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

so actually, we are looking at:

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

10=2x5 so

5^m*2^26 = 2 2^35 5^35

You can actually stop here and choose m=35. There is only one 5 on each side.