To solve the expression [tex]\(4(8-6) 5^2 - 6 \div (-3)\)[/tex], we need to follow the order of operations carefully. This order is commonly remembered using the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Here's the step-by-step solution:
1. Parentheses: Solve the expression inside the parentheses first.
[tex]\[
8 - 6 = 2
\][/tex]
Now, the expression is [tex]\(4(2) 5^2 - 6 \div (-3)\)[/tex].
2. Multiplication (implicit): Evaluate multiplication indicated by juxtaposition (just next to each other without a visible multiplication sign).
[tex]\[
4 \cdot 2 = 8
\][/tex]
Now, the expression is [tex]\(8 \cdot 5^2 - 6 \div (-3)\)[/tex].
3. Exponents: Evaluate the exponent [tex]\(5^2\)[/tex].
[tex]\[
5^2 = 25
\][/tex]
Now, the expression is [tex]\(8 \cdot 25 - 6 \div (-3)\)[/tex].
4. Multiplication: Perform the multiplication.
[tex]\[
8 \cdot 25 = 200
\][/tex]
Now, the expression is [tex]\(200 - 6 \div (-3)\)[/tex].
5. Division: Perform the division.
[tex]\[
-6 \div (-3) = 2
\][/tex]
Now, the expression is [tex]\(200 - 2\)[/tex].
6. Subtraction: Finally, perform the subtraction.
[tex]\[
200 - 2 = 198
\][/tex]
However, the problem specifically asks what is the last step in the given operations. In this case, the last calculation is:
[tex]\[
200 - (-2) \rightarrow 200 - (-(-2)) \rightarrow 200 + 2
\][/tex]
Therefore, the result for the expression, and particularly the last calculation, involves resolving [tex]\(200 - (-2)\)[/tex] correctly yielding [tex]\(200 + 2 = 202\)[/tex].
Hence, the detailed computation confirms that the last calculation was [tex]\(200 - (-2)\)[/tex], and the ultimate answer is [tex]\(200 - (-2) = 202\)[/tex].
