2.05(-64.4)$$ ^{}^2 $$-2840/1.61$$ ^3\text{ }+\text{ } $$0.664$$ ^5\text{ } $$(26.6$$ ^3 $$-9.02$$ ^4 $$) evaluate the given expression, all numbers are approximate

To evaluate the expression step by step, we will break it down into parts:

### Expression:
\[
2.05(-64.4)^2 - \frac{2840}{1.61^3} + 0.664^5(26.6^3 - 9.02^4)
\]

Let's solve this step by step:

1. **Evaluate $ (-64.4)^2 $**:
   \[
   (-64.4)^2 = 4147.36
   \]
   Then multiply by 2.05:
   \[
   2.05 \times 4147.36 = 8502.088
   \]

2. **Evaluate $ \frac{2840}{1.61^3} $**:
   First, calculate $ 1.61^3 $:
   \[
   1.61^3 = 4.163681
   \]
   Now divide:
   \[
   \frac{2840}{4.163681} \approx 682.125
   \]

3. **Evaluate $ 0.664^5 $**:
   \[
   0.664^5 = 0.0921904953
   \]

4. **Evaluate $ 26.6^3 $ and $ 9.02^4 $**:
   \[
   26.6^3 = 18809.096
   \]
   \[
   9.02^4 = 6606.553
   \]
   Subtract:
   \[
   18809.096 - 6606.553 = 12202.543
   \]

5. **Multiply $ 0.664^5 \times (26.6^3 - 9.02^4) $**:
   \[
   0.0921904953 \times 12202.543 \approx 1124.963
   \]

6. **Final Calculation**:
   Combine all terms:
   \[
   8502.088 - 682.125 + 1124.963 = 8944.926
   \]

Thus, the value of the given expression is approximately **8944.93**.

---

Would you like further clarification or details on any step? 

### 5 Related Questions:
1. How does squaring a negative number affect the result?
2. Why does exponentiation grow faster than multiplication?
3. What are the typical rounding rules when dealing with approximate numbers?
4. How can cube roots and fourth powers be calculated more easily?
5. Why are powers of fractions like $ 0.664^5 $ often very small?

**Tip:** When evaluating complex expressions, break them down into smaller steps to minimize errors.

2.05(-64.4)^2 - 2840/1.61^3 + 0.664^5(26.6^3 - 9.02^4) evaluate the given expression, all numbers are approximate

Learn how to evaluate the complex expression 2.05(-64.4)^2 - 2840/1.61^3 + 0.664^5(26.6^3 - 9.02^4) with step-by-step solutions. This problem involves exponentiation, division, and multiplication, focusing on approximate values. Suitable for students in Grades 9-12.

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