This question has been answered many times before. But there goes:
The equation provided is equivalent to (5^m)*(4^18) = 2*10^35, since all I did was "flip" the whole thing (the numerator is 1 on both sides).
Now, look at 4^18: it's actually (2^2)^18 or 2^(2*18) or 2^36.
10 = 2*5, so you get that 10^35 = (2*5)^35 = (2^35)*(5^35). Notice that 2*10^35 = 2*(2^35)*(5^35) = (2^36)*(5^35)

Replace these in the initial equation and you get that:
(5^m)*2^36 = (2^36)*(5^35). From this m is 35.

DanaJ wrote:This question has been answered many times before. But there goes:
The equation provided is equivalent to (5^m)*(4^18) = 2*10^35, since all I did was "flip" the whole thing (the numerator is 1 on both sides).
Now, look at 4^18: it's actually (2^2)^18 or 2^(2*18) or 2^36.
10 = 2*5, so you get that 10^35 = (2*5)^35 = (2^35)*(5^35). Notice that 2*10^35 = 2*(2^35)*(5^35) = (2^36)*(5^35)

Replace these in the initial equation and you get that:
(5^m)*2^36 = (2^36)*(5^35). From this m is 35.

Dana, I am getting m= -35. could you please check the answer once again?

You may be getting -35 because of the way sudi760mba wrote the equation. The correct version is, I believe:
[(1/5)^m] * [(1/4)^18] = {1/[2(10)]}^35

(1/5)^m (1/4)^18 = 1/2(10)^35
Shold be like

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

Now solve it, you will get m=35