To solve the expression [tex]\((-5)^2 + 12 \div 3 \times 2\)[/tex] using the order of operations, we follow the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Let's break it down step-by-step:
1. Exponentiation: Calculate the exponent part first.
[tex]\[ (-5)^2 \][/tex]
Squaring [tex]\(-5\)[/tex] results in:
[tex]\[ (-5) \times (-5) = 25 \][/tex]
2. Division and Multiplication: Next, perform the division and multiplication from left to right.
[tex]\[ 12 \div 3 \times 2 \][/tex]
First, divide 12 by 3:
[tex]\[ 12 \div 3 = 4 \][/tex]
Now, take that result and multiply it by 2:
[tex]\[ 4 \times 2 = 8 \][/tex]
3. Addition: Finally, add the results from the exponentiation and the division/multiplication steps.
[tex]\[ 25 + 8 \][/tex]
Adding these together gives:
[tex]\[ 25 + 8 = 33 \][/tex]
So, the correct solution to the expression [tex]\((-5)^2 + 12 \div 3 \times 2\)[/tex] is [tex]\(33\)[/tex].
Therefore, the correct answer is:
c.) 33
