To simplify the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex], we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
1. Division: First, we perform the division operation.
[tex]\[
6 \div 3 = 2
\][/tex]
2. Exponents: Next, we calculate the exponent.
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication: Then, we multiply the result from the exponentiation by 4.
[tex]\[
9 \cdot 4 = 36
\][/tex]
4. Order of Operations in Expression: Now, we follow the sequence from left to right performing addition and subtraction.
[tex]\[
2 + 36 - 2
\][/tex]
5. Addition: Perform the addition.
[tex]\[
2 + 36 = 38
\][/tex]
6. Subtraction: Finally, perform the subtraction.
[tex]\[
38 - 2 = 36
\][/tex]
Hence, the simplified result of the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex] is 36.
Therefore, the correct answer is:
A. 36
