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I see that you've uploaded a page with several math problems focused on evaluating expressions and expressing the results in scientific notation. I'll start by solving the first few, and then I can continue or explain further if needed.

1. **(5.8 × 10^3) * (6.4 × 10^5)**  
   Multiply the coefficients:  
   \( 5.8 \times 6.4 = 37.12 \)  
   Add the exponents:  
   \( 10^3 \times 10^5 = 10^{8} \)  
   So the result is:  
   \( 37.12 \times 10^8 \)  
   In scientific notation:  
   \( 3.712 \times 10^9 \)

2. **(3.92 × 10^6) / (2.2 × 10^3)**  
   Divide the coefficients:  
   \( 3.92 / 2.2 = 1.7818 \)  
   Subtract the exponents:  
   \( 10^6 / 10^3 = 10^{3} \)  
   So the result is:  
   \( 1.7818 \times 10^3 \)  
   In scientific notation:  
   \( 1.78 \times 10^3 \)

3. **(2.952 × 10^4) / (3.6 × 10^2)**  
   Divide the coefficients:  
   \( 2.952 / 3.6 = 0.82 \)  
   Subtract the exponents:  
   \( 10^4 / 10^2 = 10^{2} \)  
   So the result is:  
   \( 0.82 \times 10^2 \)  
   In scientific notation:  
   \( 8.2 \times 10^1 \)

Would you like me to continue solving the rest, provide further details on these steps, or clarify any part of the process?

Here are 5 relative questions for further exploration:
1. How do you simplify multiplication of numbers in scientific notation?
2. How do you handle division with scientific notation?
3. What steps should be taken to convert a number back into scientific notation if it's not in standard form?
4. How can you add or subtract numbers in scientific notation effectively?
5. Why do you need to adjust the coefficients in scientific notation to fit the form \( a \times 10^n \)?

**Tip:** When dividing or multiplying powers of ten, always focus on adding or subtracting the exponents, and don't forget to adjust the coefficient back into standard scientific notation if needed.

Evaluate each expression. Express the result in scientific notation.

This exercise involves evaluating multiple expressions and expressing the results in scientific notation. It covers key concepts such as the multiplication and division of exponents and basic arithmetic, suitable for students in Grades 8-10.

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