To simplify the equation \( \frac{3^3 \cdot 3^{-2}}{(3^6)^2} \), we will follow the rules of exponents.
First, simplify the numerator:
\[ 3^3 \cdot 3^{-2} = 3^{3 + (-2)} = 3^{3 - 2} = 3^1 = 3 \]
Now, simplify the denominator:
\[ (3^6)^2 = 3^{6 \cdot 2} = 3^{12} \]
Now, substitute the simplified numerator and denominator back into the expression:
\[ \frac{3^1}{3^{12}} = 3^{1 - 12} = 3^{-11} \]
Finally, \( 3^{-11} \) can be expressed as:
\[ \frac{1}{3^{11}} \]
So, the simplified form of the original equation is:
\[ \frac{1}{3^{11}} \]