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The given function is \( f_{25}(x) = \sum_{i=1}^{D} |x_i| + \prod_{i=1}^{D} |x_i| \), where \( x = \{20, -10, 50\} \) and \( D = 3 \), since the vector \( x \) has 3 components. This expression involves the sum of the absolute values of the components of \( x \) and the product of those absolute values.

### Step-by-step solution:

1. **Sum of absolute values**:
   \[
   \sum_{i=1}^{D} |x_i| = |20| + |-10| + |50| = 20 + 10 + 50 = 80
   \]

2. **Product of absolute values**:
   \[
   \prod_{i=1}^{D} |x_i| = |20| \times |-10| \times |50| = 20 \times 10 \times 50 = 10,000
   \]

3. **Final result**:
   \[
   f_{25}(x) = 80 + 10,000 = 10,080
   \]

Thus, the result of evaluating \( f_{25}(x) \) for \( x = \{20, -10, 50\} \) is **10,080**.

Would you like further details or have any questions?

### Related Questions:
1. What happens if one of the values of \( x \) is zero in this function?
2. How does the result change if all values of \( x \) are negative?
3. Can you describe how this function behaves for large values of \( D \)?
4. What does the sum and product of absolute values represent in geometrical terms?
5. How would the function change if the absolute values were not used?

### Tip:
When solving problems involving sums and products, it's always helpful to break them into smaller steps like we did here for clarity.

Diga cuál es el resultado de evaluar x = {20, -10, 50} en la función f_25(x) = ∑_{i=1}^{D} |x_i| + ∏_{i=1}^{D} |x_i|.

Learn how to evaluate the function f_25(x) = ∑_{i=1}^{D} |x_i| + ∏_{i=1}^{D} |x_i| for x = {20, -10, 50}. This problem involves calculating the sum and product of absolute values and is suitable for students in Grades 10-12.

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