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Let me assist you in solving the questions shown in the image. I'll go through each one and provide a clear answer. I'll focus on a few questions for now and work my way through the rest step by step.

### 19. Simplifying a rational expression means:
The question asks what simplifying a rational expression entails. Simplifying involves reducing the expression by canceling common factors.

- **Answer: (b) Expression reduced**

### 20. A term that could be expressed as a ratio is:
The term that represents the idea of expressing as a ratio is **fraction**.

- **Answer: (d) Fraction**

### 21. Which one is a perfect square?
A perfect square is a number that can be expressed as the square of another integer. 

- \(8\), \(9\), \(15\), and \(20\) are options.
- \(9\) is a perfect square because \(3^2 = 9\).

- **Answer: (b) 9**

### 22. Which is equal to \((m^3 n^7)^2\)?
- Simplifying \((m^3 n^7)^2\), we get \(m^{3 \cdot 2} n^{7 \cdot 2} = m^6 n^{14}\).

- **Answer: (a) \(m^6 n^{14}\)**

### 23. What is the value of \(\frac{32}{24} \times 125\)?
We can solve this expression step by step:
- First simplify \(\frac{32}{24} = \frac{4}{3}\).
- Then calculate \(\frac{4}{3} \times 125 = \frac{4 \times 125}{3} = \frac{500}{3}\).

- **Answer: (d) 166.67**

Would you like me to continue with the remaining questions? Also, here are some follow-up questions based on what we've covered:

1. How do you identify a perfect square from a set of numbers?
2. Why is simplifying rational expressions important in algebra?
3. How would you simplify more complex rational expressions?
4. Can you explain the difference between a factor and a product in terms of ratios?
5. What is the process of exponentiation when working with variables?

**Tip:** When simplifying rational expressions, always look for common factors to reduce both the numerator and the denominator.

Solve algebra problems on simplifying rational expressions, exponents, and identifying perfect squares. Includes step-by-step solutions to expressions involving fractions and exponentiation. Suitable for Grades 8-10.

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