\( \left\{\left(\left[3^{4}-6 \times 5 \div 3\right] \times 6\right) \div \sqrt{9} \div 2\right\} \times \sqrt{16} \) \( \begin{array}{lll}\text { A) } 194 & \text { B) } 284 & \text { C) } 304 \\ \text { D) } 424 & & \text { E) } 514\end{array} \)

To solve the expression, let's break it down step by step: 1. **Calculate the Innermost Expression:** \[ 3^{4} - 6 \times 5 \div 3 \] Start with \(3^{4} = 81\). Next, calculate \(6 \times 5 = 30\) and then \(30 \div 3 = 10\). Thus: \[ 3^{4} - 6 \times 5 \div 3 = 81 - 10 = 71 \] 2. **Continue the Expression:** Now substitute back into the larger expression: \[ \left(71 \times 6\right) \div \sqrt{9} \div 2 \] First compute \(71 \times 6 = 426\). 3. **Next Step:** Calculate \(\sqrt{9} = 3\): \[ 426 \div 3 = 142 \] Now divide by 2: \[ 142 \div 2 = 71 \] 4. **Final Step:** Now we need to multiply this result by \(\sqrt{16}\): \[ 71 \times \sqrt{16} = 71 \times 4 = 284 \] Thus, the final result is \(284\). So the answer is \( \text{B) } 284 \).