To simplify the expression [tex]\( 15 \div 3 + 3^2 - 4 \cdot 2 \)[/tex], we follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Division:
[tex]\[
15 \div 3 = 5
\][/tex]
2. Exponentiation:
[tex]\[
3^2 = 9
\][/tex]
3. Multiplication:
[tex]\[
4 \cdot 2 = 8
\][/tex]
Now, substitute these results back into the expression:
[tex]\[
5 + 9 - 8
\][/tex]
4. Addition and Subtraction (from left to right):
- First, perform the addition:
[tex]\[
5 + 9 = 14
\][/tex]
- Next, perform the subtraction:
[tex]\[
14 - 8 = 6
\][/tex]
Therefore, the simplified result of the expression [tex]\( 15 \div 3 + 3^2 - 4 \cdot 2 \)[/tex] is [tex]\( 6 \)[/tex].
