Question

I need a genuine answer. Don't answer if you don't know. Need a proper explanation.​

Answer 1

Explanation:

If m and n are both 1 then

Minimum value = 10^(1+1) * 3^(1-1) * 225

= 325.

If m and n have to be different, then m = 2 and n = 1

Minimum value = 10^3 * 3^1 * 15^2

= 675,000.

Answer 2

Since m and n are natural numbers then N will always be rational.
If m >= n then N will also be natural which is a subset of rational numbers.
If m < n then 3^(m - n) will be less than 1 and N will need to be written as a fraction, which are still rational.

The minimum values for both m and n are 1 by definition.