To solve the expression [tex]\(4(8-6) \cdot 5^2 - 6 \div (-3)\)[/tex] using the order of operations (PEMDAS/BODMAS), let's break it down step-by-step.
1. Parentheses/Brackets: Solve the operations inside parentheses first.
[tex]\[
4(8-6) \cdot 5^2 - 6 \div (-3)
\][/tex]
[tex]\[
= 4 \cdot 2 \cdot 5^2 - 6 \div (-3)
\][/tex]
2. Exponents/Orders: Calculate the exponent next.
[tex]\[
= 4 \cdot 2 \cdot 25 - 6 \div (-3)
\][/tex]
3. Multiplication/Division: Perform multiplication and division from left to right.
[tex]\[
= 4 \cdot 2 \cdot 25 - 6 \div (-3)
\][/tex]
[tex]\[
= 200 - 6 \div (-3)
\][/tex]
Divide [tex]\(6\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
= 200 - (-2)
\][/tex]
4. Addition/Subtraction: Finally, perform the addition or subtraction.
[tex]\[
= 200 + 2
\][/tex]
The last operation to do is to add [tex]\(200\)[/tex] and [tex]\(2\)[/tex]. Therefore, the last calculation that should be done to evaluate the expression is:
[tex]\[
\text{Add } 200 \text{ and } 2
\][/tex]
