5000 + 484218.07 * (0.002 * 4560 * (5566.18 - 340) / 340)

To solve the expression \(5000 + 484218.07 \cdot (0.002 \cdot 4560 \cdot \frac{5566.18 - 340}{340})\), we need to follow the order of operations (PEMDAS/BODMAS):

1. **Parentheses/Brackets**
2. **Exponents/Orders**
3. **Multiplication and Division** (from left to right)
4. **Addition and Subtraction** (from left to right)

Let's break it down step by step:

1. **Calculate inside the innermost parentheses**:
   \[
   5566.18 - 340 = 5226.18
   \]

2. **Division within the parentheses**:
   \[
   \frac{5226.18}{340} = 15.371117647058823
   \]

3. **Multiplication within the parentheses**:
   \[
   0.002 \cdot 4560 \cdot 15.371117647058823 = 0.002 \cdot 7003.6994117647055 = 14.007398823529412
   \]

4. **Multiplication outside the parentheses**:
   \[
   484218.07 \cdot 14.007398823529412 = 6783157.874349234
   \]

5. **Addition**:
   \[
   5000 + 6783157.874349234 = 6788157.874349234
   \]

So, the value of the given expression is approximately \(6788157.87\).

Would you like more details or have any questions? Here are some questions you might want to ask:

1. How do you handle more complex expressions?
2. Can you explain the steps in detail for solving algebraic equations?
3. What are some common mistakes to avoid in order of operations?
4. Can you solve this problem using a different method?
5. How do you simplify expressions involving multiple variables?

**Tip:** Always remember to follow the order of operations (PEMDAS/BODMAS) to avoid mistakes in calculations.

Learn how to solve the mathematical expression 5000 + 484218.07 * (0.002 * 4560 * (5566.18 - 340) / 340) step-by-step. Understand the order of operations (PEMDAS/BODMAS) and how to apply them correctly in arithmetic calculations. Suitable for high school students and above.

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