https://file.aiquickdraw.com/mathbot/file/1727384930352j2wug0qi.jpg

The image you uploaded appears to contain a sequence of steps involving scientific notation and powers of 10, likely simplifying and converting values to a common base for further calculations. I will provide a brief breakdown of what I observe in the image:

1. **Problem I:**
   \[
   609 \cdot 10^{10} \, \text{km}^2
   \]

2. **Problem II:**
   \[
   0.004 \cdot 10^{10} = \frac{4 \cdot 10^{10}}{1000} = 4 \cdot 10^{7}
   \]
   This step simplifies a small value in scientific notation.

3. **Problem III:**
   \[
   4200 \cdot 10^{10} = 42 \cdot 10^{12}
   \]

4. **Problem IV:**
   \[
   4809054 \cdot 10^{10} = \frac{4809054 \cdot 10^{10}}{1000} = 4809054 \cdot 10^{7}
   \]
   Here, the number is divided by 1000 to adjust the exponent.

5. **Converting to \(10^7\) format:**
   The image shows how each expression is simplified to powers of \(10^7\):
   - \(609 \cdot 10^{10} = 609000 \cdot 10^7\)
   - \(4 \cdot 10^7\)
   - \(42 \cdot 10^{12} = 4200000 \cdot 10^7\)
   - \(4809054 \cdot 10^7\)

   Summing these:
   \[
   609000 \cdot 10^7 + 4 \cdot 10^7 + 4200000 \cdot 10^7 = 4809004 \cdot 10^7
   \]

6. **Final Calculation:**
   After simplifying and subtracting:
   \[
   4809054 \cdot 10^7 - 4809004 \cdot 10^7 = 50 \cdot 10^7
   \]
   The answer is \(x = 50 \cdot 10^7\), which is then simplified to \(x = 0.05 \cdot 10^{10} = 5 \cdot 10^8\).

Would you like further clarification on any step, or should I explain one in detail?

### 5 Related Questions:
1. How do you convert a large number into scientific notation?
2. Why is it important to express all terms in the same power of ten during calculations?
3. What are the steps to divide numbers in scientific notation?
4. How can you simplify large numbers in calculations like this?
5. How does subtracting powers of 10 work in scientific notation?

**Tip:** Always align terms to the same exponent when adding or subtracting in scientific notation for easier calculations.

How can scientific notation be used to simplify calculations involving large and small numbers, and how are terms aligned for addition and subtraction?

This guide explains how to use scientific notation to simplify calculations with large and small numbers. Learn how to convert numbers to powers of 10, align terms for addition and subtraction, and handle operations efficiently. Perfect for high school students in Grades 9-12.

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