https://file.aiquickdraw.com/mathbot/file/1725978024338o33w1c0d.jpg

Let's solve the problems from the image one by one.

1. **\( 2.5 + 3^2 \times 0.5 \)**
   - First, calculate the exponent and multiplication: \( 3^2 = 9 \), and \( 9 \times 0.5 = 4.5 \).
   - Now, add: \( 2.5 + 4.5 = 7 \).
   - **Answer: 7**

2. **\( (-4) \times \left( \frac{3}{5} \right)^2 + 1.2 \)**
   - First, calculate the square: \( \left( \frac{3}{5} \right)^2 = \frac{9}{25} \).
   - Multiply: \( (-4) \times \frac{9}{25} = -\frac{36}{25} = -1.44 \).
   - Now, add: \( -1.44 + 1.2 = -0.24 \).
   - **Answer: -0.24**

3. **\( 6 \div (2 + 0.25^2) - 3 \)**
   - First, calculate \( 0.25^2 = 0.0625 \), then add: \( 2 + 0.0625 = 2.0625 \).
   - Now, divide: \( 6 \div 2.0625 \approx 2.91 \).
   - Subtract: \( 2.91 - 3 = -0.09 \).
   - **Answer: -0.09**

4. **\( \frac{1}{2} \times 3^3 - 1.5^2 \)**
   - First, calculate the cube and the square: \( 3^3 = 27 \) and \( 1.5^2 = 2.25 \).
   - Now, multiply: \( \frac{1}{2} \times 27 = 13.5 \).
   - Subtract: \( 13.5 - 2.25 = 11.25 \).
   - **Answer: 11.25**

5. **\( (4.5 + 2) \times \left( \frac{2}{3} \right)^2 - 1 \)**
   - First, calculate the square: \( \left( \frac{2}{3} \right)^2 = \frac{4}{9} \).
   - Add: \( 4.5 + 2 = 6.5 \).
   - Multiply: \( 6.5 \times \frac{4}{9} = \frac{26}{9} \approx 2.89 \).
   - Subtract: \( 2.89 - 1 = 1.89 \).
   - **Answer: 1.89**

6. **\( 3.5 + (-2)^3 \div \left( \frac{1}{4} \right) \)**
   - First, calculate the cube: \( (-2)^3 = -8 \).
   - Now, divide: \( -8 \div \frac{1}{4} = -8 \times 4 = -32 \).
   - Add: \( 3.5 + (-32) = -28.5 \).
   - **Answer: -28.5**

7. **\( \left( \frac{5}{6} \right)^2 \times 3.5 + 2^2 \div 4 \)**
   - First, calculate the square: \( \left( \frac{5}{6} \right)^2 = \frac{25}{36} \) and \( 2^2 = 4 \).
   - Now, multiply: \( \frac{25}{36} \times 3.5 = \frac{87.5}{36} \approx 2.43 \).
   - Divide: \( 4 \div 4 = 1 \).
   - Add: \( 2.43 + 1 = 3.43 \).
   - **Answer: 3.43**

8. **\( \frac{7}{2} \div (0.5^2 + 2) \times (-3) \)**
   - First, calculate \( 0.5^2 = 0.25 \), then add: \( 0.25 + 2 = 2.25 \).
   - Now, divide: \( \frac{7}{2} \div 2.25 = \frac{7}{2} \times \frac{4}{9} = \frac{28}{18} \approx 1.56 \).
   - Multiply: \( 1.56 \times (-3) = -4.68 \).
   - **Answer: -4.68**

9. **\( 1.2 \times (-3^2) + \left( \frac{4}{5} \right)^2 \)**
   - First, calculate the square: \( (-3)^2 = 9 \) and \( \left( \frac{4}{5} \right)^2 = \frac{16}{25} = 0.64 \).
   - Multiply: \( 1.2 \times 9 = 10.8 \).
   - Now, add: \( 10.8 + 0.64 = 11.44 \).
   - **Answer: 11.44**

10. **\( (-5)^2 + \left( \frac{3}{4} \div 1.5 \right)^3 \)**
    - First, calculate the square and cube: \( (-5)^2 = 25 \).
    - Now, divide: \( \frac{3}{4} \div 1.5 = \frac{3}{4} \times \frac{2}{3} = \frac{1}{2} \).
    - Cube: \( \left( \frac{1}{2} \right)^3 = \frac{1}{8} = 0.125 \).
    - Add: \( 25 + 0.125 = 25.125 \).
    - **Answer: 25.125**

Would you like more details or clarifications on any specific step? 

Here are 5 related questions to deepen your understanding:
1. How would the result change in problem 2 if the fraction \( \frac{3}{5} \) was squared after multiplying by \( -4 \)?
2. In problem 3, how would the expression change if you replaced division with multiplication?
3. Can you generalize the process for simplifying expressions involving fractions like in problem 5?
4. How can you verify the result of problem 6 using alternative methods of dividing fractions?
5. What happens if the signs of all terms are flipped in problem 9?

**Tip**: Always perform operations inside parentheses and exponents before handling multiplication, division, and addition/subtraction in a complex expression.

Solve 10 math expressions involving addition, multiplication, exponents, and fractions.

This guide walks through solving 10 complex math expressions that include operations like exponents, fractions, and multiplication. Learn the detailed step-by-step process, suitable for students in Grades 8-10.

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