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In the image you uploaded, there is a mathematical expression that reads:

\[ 640 \div \left( \frac{1}{2} - (-128) \right) \]

Let's solve this step-by-step.

1. **Evaluate the expression inside the parentheses**:
   \[ \frac{1}{2} - (-128) = \frac{1}{2} + 128 \]
   To add a fraction to a whole number, convert the whole number into a fraction:
   \[ \frac{1}{2} + \frac{256}{2} = \frac{257}{2} \]

2. **Divide by the result**:
   \[ 640 \div \frac{257}{2} = 640 \times \frac{2}{257} \]
   Multiply 640 by 2, then divide by 257:
   \[ \frac{1280}{257} \approx 4.98 \]

So, the solution is approximately **4.98**. 

Would you like more details on any of the steps, or do you have any other questions?

Here are some follow-up questions you might consider:
1. How do you convert a whole number to a fraction?
2. Why do we invert the fraction when dividing?
3. How would the solution change if the sign of 128 were positive?
4. What are the benefits of simplifying expressions before performing operations?
5. Can you explain more about the properties of division and multiplication with fractions?

Tip: When working with fractions, always consider simplifying them early in your calculations to make the arithmetic easier to handle.

Learn how to solve the exponentiation problem involving positive and negative bases with fractional exponents: (128)^(1/7) + (-128)^(2/7). The solution covers key concepts such as exponents, negative bases, and order of operations. Suitable for high school students, Grades 9-12.

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