LHS:
(1/5)^m = (1^m)/(5^m) = 1/(5^m)
(1/4)^18 = (1^18)/(4^18) = 1/(4^18) = 1/(2^36)

RHS:
1/2(10)^35

so, we got the following equation.
[1/(5^m)][1/(2^36)] = 1/2(10)^35
(5^m)(2^36) = 2(10)^35
(5^m)(2)(2^35) = 2(10)^35
(5^m)(2^35) = 10^35
(5^m)(2^35) = (5^35)(2^35)

if m = 35, the equation is satisfied.