Answer:
Simplifying the expression gives;
[tex]\frac{1}{3^5}[/tex]Explanation:
Given the expression:
[tex]\frac{3^{-9}\cdot3^{12}}{3^6\cdot3^2}[/tex]Applying the rules of exponent;
[tex]\begin{gathered} \frac{3^{-9}\cdot3^{12}}{3^6\cdot3^2}=\frac{3^{-9+12}}{3^{6+2}}=\frac{3^3}{3^8} \\ \end{gathered}[/tex]Solving further;
[tex]\frac{3^3}{3^8}=3^3\cdot3^{-8}=3^{3-8}=3^{-5}=\frac{1}{3^5}[/tex]Therefore, simplifying the expression gives;
[tex]\frac{1}{3^5}[/tex]