If $$m$$ and $$n$$ are natural numbers such that $$n > 1$$, and $$m^n = 2^{25} \times 3^{40}$$, then $$m - n$$ equals

We must bring the right-hand side in the form so that everything has the same power. 

25 has factors 1, 5 and 25
The only common factor 40 and 25 have is 5 (other than 1 of course, which does not work)

So the right-hand side can be rewritten as $$\left(2^5\right)^5\times\ \left(3^8\right)^5$$
$$\left(32\times\ 81\times\ 81\right)^5$$
$$\left(209952\right)^5$$

Giving the value of m - n as 209952 - 5 = 209947

Therefore, Option D is the correct answer.