If (1/5)^m * (1/4)^18 = 1 / (2 * (10)^35), what's the value of m?

(1/5)^m = 1/5^m

1 to the power of anything equals 1

(1/4)^18 = 1/4^18 (4=2^2) so 1/4^18 = 1/2^36

now we have the following:

1/5^m x 1/2^36 = 1/(2x10^35)

Because every denominator is under 1 we can set the denominators to equal each other:

5^m x 2^36 = 2 x 10^35

10^35 = 2^35 x 5^35 so now we get the following

5^m x 2^36 = 2 x 2^35 x 5^35 note the 2 x 2^35 = 2^1 x 2^35 = 2^36

5^m x 2^36 = 2^36 x 5^35
we can cancel out the 2^36 on both sides.
5^m = 5^35

m=35

Hope that helps.