Im trying to find what I got wrong in simplifying The question states " Simplify: $$\frac{6\left ( 27^{2n+3} \right )}{9^{3n+6}}$$
What I did was factoring $9$ and and $27$ to make it $3$. In the end I got a $\frac{6}{27}$ answer, simplified: $\frac{2}{9}$. but my problem is that in the book, the answer is stated as $\frac{27}{2}$. What could be the solution?

$$\frac{6 \cdot27^{2n+3}}{9^{3n+6}}=\frac{2\cdot3\cdot[(3^3)]^{2n+3}}{(3^2)^{3n+6}}$$
$$=\frac{2\cdot3\cdot3^{6n+9}}{3^{6n+12}}=\frac{2\cdot3}{3^3}=\frac2{3^2}$$
