To solve the expression [tex]\(8 \times 3 + [63 \div \{18 \div 3(9 - 17 + 5 \times 2)\}]\)[/tex], we will break it down into smaller steps, simplifying inside each set of parentheses and brackets from the innermost to the outermost, as follows:
1. Simplify inside the innermost parentheses:
[tex]\[
9 - 17 + 5 \times 2
\][/tex]
Perform the multiplication first:
[tex]\[
5 \times 2 = 10
\][/tex]
So the expression becomes:
[tex]\[
9 - 17 + 10
\][/tex]
2. Simplify the addition and subtraction inside the inner parentheses:
[tex]\[
9 - 17 + 10 = (9 - 17) + 10 = -8 + 10 = 2
\][/tex]
3. Repeat the simplified term inside the curly braces:
Now we have:
[tex]\[
18 \div 3(2)
\][/tex]
Simplify the multiplication inside the curly braces:
[tex]\[
3 \times 2 = 6
\][/tex]
So now it reads:
[tex]\[
18 \div 6
\][/tex]
4. Perform the division:
[tex]\[
18 \div 6 = 3
\][/tex]
5. Use the result in the outer division within the brackets:
Now we have:
[tex]\[
63 \div 3
\][/tex]
6. Perform the outer division:
[tex]\[
63 \div 3 = 21
\][/tex]
7. Finally, complete the initial multiplication and addition:
[tex]\[
8 \times 3 + 21
\][/tex]
First, do the multiplication:
[tex]\[
8 \times 3 = 24
\][/tex]
8. Add the result:
[tex]\[
24 + 21 = 45
\][/tex]
Thus, the final result of the expression [tex]\(8 \times 3 + [63 \div \{18 \div 3(9 - 17 + 5 \times 2)\}]\)[/tex] is [tex]\(\boxed{45}\)[/tex].
