To simplify the expression [tex]\(\left[5 + 2(7) + 3^2\right] \div 2 \cdot 6\)[/tex], we need to follow the order of operations (PEMDAS/BODMAS):
1. Parentheses
2. Exponents
3. Multiplication and Division (left-to-right)
4. Addition and Subtraction (left-to-right)
Let's apply these rules step-by-step:
1. Expression inside the brackets: [tex]\(\left[5 + 2(7) + 3^2\right]\)[/tex]
Before we can simplify addition of 5 and [tex]\(2(7)\)[/tex], we need to handle the exponent first because exponents come before multiplication and addition.
2. Exponents: The exponent in the expression is [tex]\(3^2\)[/tex], which equals 9.
Therefore, the first step is to square the 3 resulting in [tex]\(3^2 = 9\)[/tex].
