To solve this problem, we need to first simplify the given equations.

We are given that 4 = 10^2m and 9 = 10^2n.

To find the value of 0.15, we can write it as a power of 10.

0.15 can be written as 15/100, which simplifies to 3/20 or (3/2)*(1/10).

Now, let`s express 3/2 and 1/10 in terms of powers of 10.

3/2 can be written as (10^1.5)/(10^1), and 1/10 can be written as 10^(-1).

Multiplying these two fractions, we get (10^1.5)*(10^(-1)) = 10^(1.5 - 1) = 10^0.5.

Comparing this with the given options, we see that the correct answer is option 4: 10^(n-m-1).

This is because the value of 0.15 can be expressed as 10^(1.5 - 0) = 10^(n-m-1).

Therefore, option 4 is