Simplify: $3!(2^3+\sqrt{9})\div 2$.
To simplify this expression, I need to apply the order of operations and follow the rules of arithmetic. I also need to recall what the factorial notation means: $n!$ is the product of all the positive integers from 1 to n. So, $3!$ means $3\times 2\times 1$, which is 6. Now, I can rewrite the expression as $6(2^3+\sqrt{9})\div 2$. Next, I need to evaluate the exponents and the square root. $2^3$ means $2\times 2\times 2$, which is 8. $\sqrt{9}$ means the positive number that, when squared, gives 9. That is 3. So, the expression becomes $6(8+3)\div 2$. Then, I need to simplify the parentheses by adding 8 and 3. That gives me $6(11)\div 2$. Next, I need to perform the multiplication and division, which have the same precedence, so I can do them from left to right. $6(11)$ means $6\times 11$, which is 66. $66\div 2$ means the quotient of 66 and 2, which is 33. So, the expression simplifies to 33. 