Question 1: Evaluate the value of 2⁻³.

Answer: 1/8

Question 2: Simplify the expression: a⁻² × a³.

Answer: a

Question 3: Express 5⁻⁴ as a fraction.

Answer: 1/625

Question 4: Calculate the value of (3/4)⁻².

Answer: 16/9

Question 5: If a⁻⁴ = 1/81, find the value of a.

Answer: 3

Question 6: Construct an example to demonstrate that a⁻ⁿ = 1/aⁿ using specific numbers.

Answer: For example, 2⁻³ = 1/2³ = 1/8.

Question 7: Determine the value of x if 10⁻ˣ = 1/1000.

Answer: 3

Question 8: Solve: a⁻² = 1/16. Find the possible values of a.

Answer: 4 or -4

Question 9: Explain why the expression a⁻ⁿ = 1/aⁿ makes sense when a is a positive real number.

Answer: Because negative exponents indicate reciprocal powers, so a⁻ⁿ = 1/aⁿ by definition.

Question 10: Identify and correct the mistake in this statement: 5⁻² = -1/25.

Answer: The correct answer is 1/25, not -1/25.

Question 11: A farmer reduces a stockpile of 100 apples by repeatedly dividing by 2. How many apples remain after 4 divisions? Express your answer using negative exponents.

Answer: 100 × 2⁻⁴ or 100/16