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.