[tex] \displaystyle\frac{2^n\cdot 2^3+2^n\cdot2^2+2^n\cdot2^1+2^n}{3^n\cdot3^2+2\cdot3^n+2\cdot3^n\cdot3^1+3^n} =\\
= \frac{2^n(8+4+2+1)}{3^n(9+6+1)} = \frac{2^n\cdot15}{3^n\cdot 16} =\\
= \frac{2^{n-1}\cdot2\cdot3\cdot5}{3^{n-1}\cdot3\cdot2\cdot8} =\\
=\frac{2^{n-1}\cdot6\cdot5}{3^{n-1}\cdot6\cdot8}^{(6}=\\
=\frac{2^{n-1}\cdot5}{3^{n-1}\cdot8}[/tex]
