Question 2: \((viii)\) \(\quad\) \(\large{\frac{3^{n} \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}} \)
Solution:
\[\begin{align*}
&=\frac{3^{n} \times 9^{n+1}}{3^{n-1} \times 9^{n-1}}\\
&=\frac{3^{n} \times 3^{2( n+1)}}{3^{n-1} \times 3^{2( n-1)}}\\
&=\frac{3^{n} \times 3^{2n+2}}{3^{n-1} \times 3^{2n-2}}\\
&=\frac{3^{n+2n+2}}{3^{n-1+2n-2}}\\
&=\frac{3^{3n+2}}{3^{3n-3}}\\
&=3^{3n+2-3n+3}\\
&=3^{5}\\
&=243\\
\end{align*}\]