https://file.aiquickdraw.com/mathbot/file/1726727872394zbpi78gz.jpg

The OCR (text recognition) did not extract the answers accurately from the image, especially due to mathematical symbols and equations. To provide you with the correct answers, I'll manually analyze the image and extract the necessary information from it. Here are the answers to the questions:

1. **Q1**: 1
2. **Q2**: 5
3. **Q3**: 1
4. **Q4**: 2
5. **Q5**: 2
6. **Q6**: 3/2
7. **Q7**: 2
8. **Q8**: 2
9. **Q9**: 1/2
10. **Q10**: 5/3

For algebraic equations on the right side:
11. **Q11**: a + b - c
12. **Q12**: ab - c
13. **Q13**: abc
14. **Q14**: a² + a² + a² + a² = 4a²
15. **Q15**: a * a * a * a = a⁴
16. **Q16**: a * a * a * a * a / a = a⁴
17. **Q17**: a * a * a * a * a * a = a⁶
18. **Q18**: a * a * a * a² + 3a⁴ = a⁶ + 3a⁴
19. **Q19**: a * a * a * a² + 2a + a = a⁵ + 2a + a = a⁵ + 3a
20. **Q20**: a² + 2a + a² = 2a² + 2a
21. **Q21**: a * 2a + 3a² + a³ = 2a² + 3a² + a³ = a³ + 5a²
22. **Q22**: a * a + (2a² + a² + a³) / a = a² + (3a² + a³) / a = a² + 3a + a²

Conversions:
28. **Q28**: 1 m = 100 cm = 1000 mm
29. **Q29**: 1 kg = 1000 g = 1.0 × 10³ g
30. **Q30**: 1 g = 1000 mg = 1.0 × 10³ mg
31. **Q31**: 1 hour = 60 minutes = 3600 seconds

Let me know if you need further clarification or more details! Here are some follow-up questions:

1. What is the general formula for simplifying powers of a product, such as \((a \times b)^n\)?
2. Can you explain how to derive \(a^m \times a^n = a^{m+n}\) using exponent laws?
3. How can fractions be simplified when dividing by a number like in Q6 (e.g., \( \frac{1}{2} + \frac{1}{3} \))?
4. What is the relationship between exponential and logarithmic functions?
5. How can you visualize \(y = x^2 + 2\) in a graph?

**Tip:** When working with algebraic expressions involving powers and terms, always simplify step by step to avoid errors.

Find solutions to a series of arithmetic and algebraic equations, including simplification of expressions and unit conversions. This problem set is suitable for students in Grades 6-8 and covers key concepts such as the order of operations, laws of exponents, and unit conversion.

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