To determine what should be calculated first in the given mathematical expression,
[tex]\[
[(-3) \cdot (-8) + 6] - (-6 \div (-2)),
\][/tex]
we must follow the order of operations, also known as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
1. Parentheses/Brackets:
Evaluate the expressions within the brackets first. The outer brackets contain two sub-expressions:
[tex]\[(-3) \cdot (-8) + 6\][/tex]
and
[tex]\[-(-6 \div (-2))\][/tex]
2. Inside the Brackets:
We need to focus on the operations within each of these sub-expressions separately before combining them.
3. Sub-expression Evaluation:
- Within the first sub-expression \((-3) \cdot (-8) + 6\), the multiplication \((-3) \cdot (-8)\) must be performed first.
- Within the second sub-expression \(-(-6 \div (-2))\), the division \(-6 \div (-2)\) must be performed first.
Now, we look at the options provided to determine which specific part of the expression should be calculated first:
A. \(-6 - (-6)\) - This does not appear directly within our expression and does not represent an initial step.
B. \(-6 \div (-2)\) - This division operation occurs within the sub-expression \(-(-6 \div (-2))\).
C. \((-3) \cdot (-8)\) - This multiplication operation occurs within the sub-expression \((-3) \cdot (-8) + 6\).
D. \(-8 + 6\) - This addition/subtraction operation is not directly within our expression initially in this form.
Thus, the correct first operation as per the order of operations from the given choices is:
B. [tex]\(-6 \div (-2)\)[/tex]
