To simplify the expression [tex]\( 6 \div 3 + 3^2 \cdot 4 - 2 \)[/tex], let's follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division, and Addition and Subtraction.
1. Division:
Calculate [tex]\( 6 \div 3 \)[/tex]:
[tex]\[
6 \div 3 = 2
\][/tex]
2. Exponents:
Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication:
Multiply the result of the exponentiation by 4:
[tex]\[
9 \cdot 4 = 36
\][/tex]
4. Addition and Subtraction:
Now, add the results of the division and the multiplication, then subtract 2:
[tex]\[
2 + 36 - 2 = 36
\][/tex]
Based on these calculations, the correct answer is:
C. 36
