Question

The number of pairs positive integers $(m,n)$ such that $m^n=25$ is

• A. $0$
• B. $1$
• C. $2$
• D. more than $2$

Answer 1

Answer: (C)

$2$

The only possibility of $m$ and $n$ in $m^n=25$ is $m=5$ and $n=2$ because $5^2=25$ and therefore, the only pair of positive integers $(m,n)$ is $(5,2)$ such that $m^n=25$.

Also, $m=25$ and $n=1$, so ${25}^1=25$

Hence, there are $2$ pairs.