To simplify the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex], we will follow the order of operations, often referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Division: Start with the division within the expression.
[tex]\[
6 \div 3 = 2
\][/tex]
Now the expression simplifies to:
[tex]\[
2 + 3^2 \cdot 4 - 2
\][/tex]
2. Exponentiation: Next, handle the exponentiation.
[tex]\[
3^2 = 9
\][/tex]
So, the expression now becomes:
[tex]\[
2 + 9 \cdot 4 - 2
\][/tex]
3. Multiplication: Then, perform the multiplication.
[tex]\[
9 \cdot 4 = 36
\][/tex]
Thus, the expression is now:
[tex]\[
2 + 36 - 2
\][/tex]
4. Addition and Subtraction: Finally, perform the addition and subtraction from left to right.
[tex]\[
2 + 36 = 38
\][/tex]
[tex]\[
38 - 2 = 36
\][/tex]
Therefore, the simplified value of the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex] is [tex]\( 36 \)[/tex].
The correct answer is:
A. 36
