Question

If $\frac{52}{160}=\frac{13}{2^n\times 5^m}$, then $m+n=$ ______

Answer 1

$\frac{52}{160}=\frac{13}{40}=\frac{13}{8\times 5}=\frac{13}{2^3\times 5^1}$

According to question

$\frac{13}{2^n\times 5^m}=\frac{13}{2^3\times 5^1}$

$\therefore n=3$ and $m=1$

$\therefore m+n=3+1=4$