Question 1: Simplify the expression: a³ ÷ a¹

Answer: a²

Question 2: Calculate the value of 2⁵ ÷ 2².

Answer: 2³

Question 3: If a⁴ ÷ a² = a², what is the value of a?

Answer: any real number (since a ≠ 0)

Question 4: Express as a single term: 3⁶ ÷ 3³.

Answer: 3³

Question 5: Simplify: (x⁵ y³) ÷ (x² y¹).

Answer: x³ y²

Question 6: A plant grows such that its height doubles every year. If its initial height is represented by h, write an expression for its height after n years using index laws.

Answer: h × 2ⁿ

Question 7: Construct a diagram on the grid that shows the division of 8⁴ ÷ 8² and verify the result.

Answer: 8²

Question 8: If a⁹ ÷ a⁵ = a^x, find x and explain why.

Answer: x=4

Question 9: A scientist uses the formula 5ⁿ ÷ 5³ to determine the power of 5 needed for a reaction. If the result is 5^k, express k in terms of n, and find the value of k when n=7.

Answer: k=n-3; when n=7, k=4

Question 10: Identify and correct the mistake in simplifying: a² ÷ a³ = a^5.

Answer: The correct answer is a^(-1).

Question 11: Evaluate and compare: 4⁶ ÷ 4² and 16³ ÷ 16². Are they equal? Show your reasoning.

Answer: Yes, both equal 4⁴ or 256.