To solve the given expression [tex]\(5+2^3 \cdot(22+11)-3^2 \cdot(4+5)\)[/tex], we'll follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here’s the step-by-step solution:
1. Parentheses: First, solve the expressions inside the parentheses.
[tex]\[
(22 + 11) = 33
\][/tex]
[tex]\[
(4 + 5) = 9
\][/tex]
2. Rewrite the expression with the evaluated parentheses:
[tex]\[
5 + 2^3 \cdot 33 - 3^2 \cdot 9
\][/tex]
3. Exponents: Next, we handle the exponents.
[tex]\[
2^3 = 8
\][/tex]
[tex]\[
3^2 = 9
\][/tex]
4. Rewrite the expression with the evaluated exponents:
[tex]\[
5 + 8 \cdot 33 - 9 \cdot 9
\][/tex]
5. Multiplication and Division: Now, we perform any multiplication and division from left to right.
[tex]\[
8 \cdot 33 = 264
\][/tex]
[tex]\[
9 \cdot 9 = 81
\][/tex]
6. Rewrite the expression with the evaluated multiplications:
[tex]\[
5 + 264 - 81
\][/tex]
7. Addition and Subtraction: Finally, perform addition and subtraction from left to right.
[tex]\[
5 + 264 = 269
\][/tex]
[tex]\[
269 - 81 = 188
\][/tex]
Hence, the result of the expression [tex]\( 5 + 2^3 \cdot (22 + 11) - 3^2 \cdot (4 + 5) \)[/tex] is [tex]\(\boxed{188}\)[/tex].
