Absolutely, I'd love to help you with this expression! Let's solve the given mathematical expression step-by-step:
[tex]\[ \left(18 \div 3 + \left\{4^2 - (3 + 12 \div 3)\right\} + 9 \right) \][/tex]
1. First, address the divisions within the expression.
[tex]\[ 18 \div 3 = 6 \][/tex]
2. Next, deal with the internal division:
[tex]\[ 12 \div 3 = 4 \][/tex]
3. Proceed with the addition within the nested parentheses:
[tex]\[ 3 + 4 = 7 \][/tex]
4. Now perform the exponentiation:
[tex]\[ 4^2 = 16 \][/tex]
5. Subtract the result of the addition from the result of the exponentiation:
[tex]\[ 16 - 7 = 9 \][/tex]
6. Add the result of the first division to the result of the subtraction:
[tex]\[ 6 + 9 = 15 \][/tex]
7. Finally, add the remaining number to complete the expression:
[tex]\[ 15 + 9 = 24 \][/tex]
Therefore, the value of the given expression is [tex]\(\boxed{24}\)[/tex].
