Simplify the expression. \( \left(3 u^{3} v^{6}\right)^{3}=\square \)

To simplify the expression \( \left(3 u^{3} v^{6}\right)^{3} \), we need to apply the power to each factor inside the parentheses. First, we raise the coefficient 3 to the power of 3: \( 3^{3} = 27 \). Next, we apply the power of 3 to \( u^{3} \): \( (u^{3})^{3} = u^{3 \times 3} = u^{9} \). Then, we apply the power of 3 to \( v^{6} \): \( (v^{6})^{3} = v^{6 \times 3} = v^{18} \). Putting it all together, we have: \( \left(3 u^{3} v^{6}\right)^{3} = 27 u^{9} v^{18} \). So, the simplified expression is: \[ 27 u^{9} v^{18} \]