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Let's analyze and solve the questions from the provided image.

### Questions:

1. \( \frac{2}{3} \times 6 \)
2. \( 4 \div \frac{2}{5} \)
3. \( 3 \frac{1}{4} + 2 \frac{2}{3} \)
4. \( \sqrt{81} \)
5. \( 3^2 + 4^2 \)
6. \( 9 - (4 + 3) \)
7. \( \sqrt[3]{64} \)
8. \( 1.5 \div 0.5 \)

### Solutions:

1. **\( \frac{2}{3} \times 6 \):**
   \[
   \frac{2}{3} \times 6 = \frac{2 \times 6}{3} = \frac{12}{3} = 4
   \]
   **Answer: 4**

2. **\( 4 \div \frac{2}{5} \):**
   \[
   4 \div \frac{2}{5} = 4 \times \frac{5}{2} = \frac{4 \times 5}{2} = \frac{20}{2} = 10
   \]
   **Answer: 10**

3. **\( 3 \frac{1}{4} + 2 \frac{2}{3} \):**
   Convert mixed numbers to improper fractions:
   \[
   3 \frac{1}{4} = \frac{13}{4}, \quad 2 \frac{2}{3} = \frac{8}{3}
   \]
   Find a common denominator (12):
   \[
   \frac{13}{4} = \frac{39}{12}, \quad \frac{8}{3} = \frac{32}{12}
   \]
   Add the fractions:
   \[
   \frac{39}{12} + \frac{32}{12} = \frac{39 + 32}{12} = \frac{71}{12} \approx 5.92
   \]
   **Answer: \(\frac{71}{12}\) or approximately 5.92**

4. **\( \sqrt{81} \):**
   \[
   \sqrt{81} = 9
   \]
   **Answer: 9**

5. **\( 3^2 + 4^2 \):**
   \[
   3^2 + 4^2 = 9 + 16 = 25
   \]
   **Answer: 25**

6. **\( 9 - (4 + 3) \):**
   \[
   9 - (4 + 3) = 9 - 7 = 2
   \]
   **Answer: 2**

7. **\( \sqrt[3]{64} \):**
   \[
   \sqrt[3]{64} = 4
   \]
   **Answer: 4**

8. **\( 1.5 \div 0.5 \):**
   \[
   1.5 \div 0.5 = \frac{1.5}{0.5} = 3
   \]
   **Answer: 3**

Would you like more details on any of these solutions or have any questions?

Here are 8 related questions for further exploration:

1. How do you convert mixed numbers to improper fractions?
2. Can you solve \(5 \frac{1}{2} - 2 \frac{3}{4}\)?
3. How do you find the cube root of a number?
4. What is the importance of using a common denominator when adding fractions?
5. Can you simplify \( \frac{3}{4} \times \frac{8}{5} \)?
6. How do you divide fractions by whole numbers?
7. Can you solve \(2^3 + 3^3\)?
8. What is the process for solving \(12 \div 3 \frac{1}{2}\)?

**Tip:** When working with fractions, always simplify your final answer to its lowest terms for clarity and accuracy.

Learn how to solve arithmetic and exponentiation problems with detailed step-by-step solutions. This problem set covers converting mixed numbers to improper fractions, basic arithmetic operations, exponentiation, and square roots. Suitable for students in Grades 5-8.

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