What is this expression in simplified form? \[ \begin{array}{l}3 \sqrt{3} \cdot 6 \sqrt{6} \\ \text { A. } 54 \sqrt{2} \\ \text { B. } 18 \sqrt{2} \\ \text { O C. } 18 \sqrt{3} \\ \text { D. } 54\end{array} \]

To simplify the expression \( 3 \sqrt{3} \cdot 6 \sqrt{6} \), we start by multiplying the coefficients and the square roots separately: 1. **Coefficients:** Multiply \( 3 \cdot 6 = 18 \). 2. **Square Roots:** Multiply \( \sqrt{3} \cdot \sqrt{6} = \sqrt{18} \). 3. **Now substitute \( \sqrt{18} \):** We know that \( \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3 \sqrt{2} \). So when we combine everything together: \[ 3 \sqrt{3} \cdot 6 \sqrt{6} = 18 \cdot 3 \sqrt{2} = 54 \sqrt{2} \]. Thus, the simplified form is \( \boxed{54 \sqrt{2}} \), which corresponds to option A.