$\frac{9^{n-1}}{3^{2n-3}}=\frac{(3^2{)}^{n-1}}{3^{2n-3}}=\frac{3^{2n-2}}{3^{2n-3}}=3^{2n-2-(2n-3)}=3^{2n-2-2n+3}=3^1=3$

$\frac{7^{n+1}\ast 2^{n-1}}{{14}^n}=\frac{7^{n+1}\ast 2^{n-1}}{7^n\ast 2^n}=7\ast 2^{-1}=\frac{7}{2}=3\frac{1}{2}$

$\frac{2^{2n-1}\ast 3^{n+1}}{{12}^n}=\frac{2^{2n-1}\ast 3^{n+1}}{4^n\ast 3^n}=\frac{2^{2n-1}\ast 3^{n+1}}{(2^2{)}^n\ast 3^n}=\frac{2^{2n-1}\ast 3^{n+1}}{2^{2n}\ast 3^n}=2^{-1}\ast 3=\frac{3}{2}=1\frac{1}{2}$

$\frac{a^6+a^{11}}{a^{-4}+a}=\frac{a^6(1+a^5)}{a^{-4}(1+a^5)}=a^{6-(-4)}=a^{6+4}=a^{10}$

$\frac{a^{-3}+a^{-2}+a^{-1}}{a^3+a^2+a}=\frac{a^{-3}(1+a+a^2)}{a(a^2+a+1)}=a^{-3-1}=a^{-4}=\frac{1}{a^4}$

$\frac{6^{n+2}-6^n}{35}=\frac{6^n(6^2-1)}{35}=\frac{6^n(36-1)}{35}=\frac{6^n\ast 35}{35}=6^n$

$\frac{5^{n+2}-5^{n-2}}{5^n}=\frac{5^n(5^2-5^{-2})}{5^n}=25-\frac{1}{25}=24\frac{24}{25}$

$\frac{2^{-n}+1}{2^n+1}=\frac{2^{-n}(1+2^n)}{2^n+1}=2^{-n}=\frac{1}{2^n}$