To simplify the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex], let's break down the calculation step by step, following the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Division: First, we perform the division in the expression [tex]\( 6 \div 3 \)[/tex].
[tex]\[
6 \div 3 = 2.0
\][/tex]
2. Exponentiation: Next, we calculate the power [tex]\( 3^2 \)[/tex].
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication: We then multiply the result of the exponentiation by 4.
[tex]\[
9 \cdot 4 = 36
\][/tex]
4. Addition and Subtraction: Finally, we perform the addition and subtraction operations from left to right.
[tex]\[
2.0 + 36 - 2
\][/tex]
5. Perform the addition:
[tex]\[
2.0 + 36 = 38.0
\][/tex]
6. Perform the subtraction:
[tex]\[
38.0 - 2 = 36.0
\][/tex]
Thus, the simplified result of the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex] is [tex]\( 36.0 \)[/tex].
Therefore, the correct answer is:
A. 36
