ANSWER:
C. m = -9, n = 4
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]\frac{9^m}{9^n}=9^{-5}[/tex]
Since it is always the same base, we can propose the following equation:
[tex]\begin{gathered} m-n=-5 \\ \text{ solving for m} \\ m=-5+n \end{gathered}[/tex]
We replace to confirm each option, just like this:
[tex]\begin{gathered} m=-5+13=8,\text{ they are solutions} \\ m=-5+3=-2,\text{ they are solutions} \\ m=-5+4=-1,\text{ they are NOT solutions} \\ m=-5+6=1,\text{ they are solutions} \end{gathered}[/tex]
Therefore option C are not possible values for m and n.
