Question

Which of the following are NOT possible values for m and n ?

Answer 1

C. m = -9, n = 4

Explanation:

We have the following expression:

`(9^m)/(9^n)=9^(-5)`

Since it is always the same base, we can propose the following equation:

`\begin{gathered} m-n=-5 \\ \text{ solving for m} \\ m=-5+n \end{gathered}`

We replace to confirm each option, just like this:

`\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}`

Therefore option C are not possible values for m and n.