To simplify the expression [tex]\( 6^2 \div (20 - 11) \times 4 \)[/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)).
1. Parentheses: First, we simplify the expression inside the parentheses:
[tex]\[
20 - 11 = 9
\][/tex]
Now the expression is:
[tex]\[
6^2 \div 9 \times 4
\][/tex]
2. Exponents: Next, we calculate the exponentiation:
[tex]\[
6^2 = 36
\][/tex]
So the expression now becomes:
[tex]\[
36 \div 9 \times 4
\][/tex]
3. Division and Multiplication: Finally, we perform the division and multiplication from left to right:
[tex]\[
36 \div 9 = 4
\][/tex]
Followed by:
[tex]\[
4 \times 4 = 16
\][/tex]
Thus, the simplified value of the expression [tex]\( 6^2 \div (20 - 11) \times 4 \)[/tex] is [tex]\(\boxed{16}\)[/tex].
