Answer:
[tex]3^{2-n}[/tex]
Step-by-step explanation:
Given expression in the picture is,
[tex]\frac{3^n}{9^{n-1}}[/tex]
= [tex]\frac{3^n}{(3^2)^{n-1}}[/tex]
= [tex]\frac{3^n}{3^{2(n-1)}}[/tex]
= [tex]3^n\times 3^{-2(n-1)}[/tex] [Since, [tex]\frac{a^n}{a^m}=a^n\times a^{-m}[/tex]]
= [tex]3^{n-2(n-1)}[/tex] [Since, [tex]a^m\times a^n=a^{m+n}[/tex]]
= [tex]3^{n-2n+2}[/tex]
= [tex]3^{2-n}[/tex]
Therefore, answer is [tex]3^{2-n}[/tex].
