Question 7: Simplify the following:
\((iii)\) \(\quad\) \(\large{\frac{6( 3)^{n+2}}{3^{n+1} -3^{n}}}\)
Solution:
\[
\begin{align*}
&=\frac{6( 3)^{n+2}}{3^{n+1} -3^{n}}\\
&=\frac{3\times 2\times 3^{n} \times 3^{2}}{3^{n}\left( 3^{1} -1\right)}\\
&=\frac{3\times 2\times 3^{2}}{2}\\
&=3\times 3^{2}\\
&=3\times 9\\
&=27\\
\end{align*}
\]