Comparing quantities and exponents and powers are important concepts in mathematics that are introduced in Class 7. These concepts lay the foundation for understanding higher-level mathematical operations and real-life applications. In this response, we will discuss the key topics and provide practice and HOTs (Higher Order Thinking) questions for each.

Comparing Quantities:
Comparing quantities involves understanding the relationship between two or more quantities, such as numbers, ratios, or percentages. This concept helps in analyzing data, making comparisons, and solving problems involving proportions. Here are some practice and HOTs questions for comparing quantities:

1. Practice Questions:
a. Compare the following fractions: 3/4, 5/8, 2/3.
b. If the price of a book is $20 and it is discounted by 25%, what will be the discounted price?
c. Compare the following decimals: 0.25, 0.3, 0.2.

2. HOTs Questions:
a. A car traveled 480 km in 6 hours. Another car traveled 600 km in 8 hours. Which car had a higher average speed?
b. Ramesh scored 85% in a math test, while Suresh scored 80%. Who performed better?
c. The ratio of boys to girls in a class is 3:4. If there are 24 boys, how many girls are there?

Exponents and Powers:
Exponents and powers are used to represent repeated multiplication and simplify large numbers. This concept is helpful in various mathematical calculations, including scientific notation and algebraic expressions. Here are some practice and HOTs questions for exponents and powers:

1. Practice Questions:
a. Simplify: 2^3 × 2^4.
b. Evaluate: (5^2)^3.
c. Express 0.00025 in standard form.

2. HOTs Questions:
a. Calculate the value of (3^2 ÷ 3^(-4)) × 3^(-1).
b. Express 625 as a power of 5.
c. Simplify: (2^3)^2 ÷ (2^4)^(-1).

These questions cover a range of difficulty levels and test the understanding of comparing quantities and exponents and powers. Solving these questions will help students reinforce their understanding of these concepts and develop problem-solving skills. Remember to practice regularly and seek clarification for any doubts to strengthen your knowledge in these topics.