Let's simplify the expression [tex]\( 7(13-5)^2 + 22 \div 11 \)[/tex] step-by-step using the order of operations.
1. Evaluate the expression inside the parentheses:
[tex]\[
(13 - 5)
\][/tex]
[tex]\[
13 - 5 = 8
\][/tex]
2. Evaluate the exponent:
[tex]\[
8^2
\][/tex]
[tex]\[
8^2 = 64
\][/tex]
3. Multiply by 7:
[tex]\[
7 \times 64
\][/tex]
[tex]\[
7 \times 64 = 448
\][/tex]
4. Divide 22 by 11:
[tex]\[
22 \div 11
\][/tex]
[tex]\[
22 \div 11 = 2
\][/tex]
5. Add the two terms:
[tex]\[
448 + 2
\][/tex]
[tex]\[
448 + 2 = 450
\][/tex]
Thus, the simplified value of the expression [tex]\( 7(13-5)^2 + 22 \div 11 \)[/tex] is 450.
