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 (from left to right), Addition and Subtraction (from left to right)).
Here’s the step-by-step process:
1. Division:
[tex]\[
6 \div 3 = 2
\][/tex]
2. Exponents:
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication:
[tex]\[
9 \cdot 4 = 36
\][/tex]
4. Combination of results:
[tex]\[
2 + 36 - 2
\][/tex]
5. Addition and Subtraction:
[tex]\[
2 + 36 = 38
\][/tex]
[tex]\[
38 - 2 = 36
\][/tex]
The simplified result of the expression [tex]\(6 \div 3 + 3^2 \cdot 4 - 2\)[/tex] is 36. Therefore, the correct answer is:
C. 36
