(1/5)^m * (1/4)^18 = [1/2*(10)^35]
=>(1/5)^m=2^36/(2*2^35*5^35)=2^36/(2^36*5^35)=(1/5)^35
=> m=35

hope this helps...!!

Simply break down the 10=2*5 on the right hand side;

You'll get the power of 1/5 as 35 on the Right side
Oh the left side the power of 1/5 is m
As both should be equal m=35

The use of reciprocals can make the question confusing, if you are not comfortable with reciprocals, you can write: (1/5)^m as 5^-m Then you'll be able to solve all such problems very easily.

Hope that helps!!