Question 1: Calculate the simplified form of 2⁵ ÷ 2³.

Answer: 2²

Question 2: Simplify the expression: 5⁸ ÷ 5⁵.

Answer: 5³

Question 3: Express as a single power: 3³ ÷ 3¹.

Answer: 3²

Question 4: Calculate the value of 10⁷ ÷ 10⁴.

Answer: 10³

Question 5: Simplify: (4²) ÷ (4¹).

Answer: 4¹

Question 6: If a = 7, what is the value of a⁶ ÷ a³?

Answer: 7³

Question 7: A scientist has 10⁸ molecules of a substance. How many groups of 10³ molecules can be formed? Express your answer using indices.

Answer: 10⁵

Question 8: Construct a triangle on the grid with side lengths proportional to 3⁴, 3², and 3³. Write the ratio of the sides in terms of powers of 3.

Answer: 3⁴ : 3² : 3³

Question 9: A bacteria population doubles every hour. The initial population is 2³. Write an expression for the population after 4 hours, using indices.

Answer: 2³ × 2⁴ = 2⁷

Question 10: Calculate the value of (8²) ÷ (8⁰).

Answer: 8²

Question 11: Explain why dividing two powers with the same base results in subtracting the exponents.

Answer: Because using the law aᵐ ÷ aⁿ = aᵐ⁻ⁿ, the exponents are subtracted when dividing powers of the same base.

Question 12: An engineer reduces the power of a circuit component from 10⁶ to 10³. How many times has the power been reduced? Express your answer as an index.

Answer: 10³

Question 13: Identify and correct the mistake in simplifying: 2⁵ ÷ 2³ = 2⁸.

Answer: The correct answer is 2², not 2⁸. The mistake is adding exponents instead of subtracting.