Question 2.

It is given that there are exactly 41 numbers, which can be expressed as the power of two, and exist between $8^m$ and $8^n$, (where m, and n are positive integers, and m < n)

Hence, $2^{3m}$ < 41 numbers < $2^{3n}$

Since, m is a positive integer, the least value of m is 1. Therefore, $2^{3m}$ = $2^3$, hence, the 41 numbers between them are $2^4$, $2^5$, $2^6$, ..., $2^{44}$

Then the lowest possible value of $8^n$ is $2^{45}$. Hence, the smallest value of n is $2^{45}$ = $8^n$ => $2^{3n}$ = $2^{45}$ => n = 15

Hence, the smallest value of m+n is (15+1) = 16