Question

If $m^n.n^m=800,m<n$, then the value of $\frac{n}{m}$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{5}$
• C. $\frac{4}{5}$
• D. $\frac{5}{2}$

Answer 1

The correct option is D $\frac{5}{2}$

$800=2\times 2\times 2\times 2\times 2\times 5\times 5$

$=2^5\times 2^2$
$\therefore m^n.n^m=800=2^5{.5}^2$
$\Rightarrow m=2,n=5$

$\therefore \frac{n}{m}=\frac{5}{2}$