Question 1: Evaluate the expression: 3² × 2³

Answer: 72

Question 2: Simplify: (5³) ÷ (5¹)

Answer: 25

Question 3: Calculate: (2⁴) × (2⁵)

Answer: 512

Question 4: Evaluate: 10³ + 10²

Answer: 1100

Question 1: Evaluate (2³)² and explain why the result is different from 2⁶.

Answer: Because (2³)² = 2³ × 2³ = 2⁶, but the process involves applying the power rule. The result is 64.

Question 2: Simplify and evaluate: (4² × 4³) ÷ 4⁴.

Answer: 4¹

Question 3: If x = 3, evaluate x⁴ ÷ x² and justify your answer.

Answer: x² or 9, because x⁴ ÷ x² = x⁴⁻² = x² = 9.

Question 1: A bacteria population doubles every hour. If it starts with 5 bacteria, how many bacteria are there after 4 hours? Write the expression using index notation and evaluate.

Answer: 80

Question 2: A savings account accrues interest at a rate of 5% per year. After 3 years, what is the growth factor? Use index notation and evaluate.

Answer: 1.157625

Question 1: Evaluate the expression: (2⁻³)⁴ and explain the rule used.

Answer: 2⁻¹²

Question 2: Construct a number in index notation that has a value of 1/16. Write your answer and justify your choice.

Answer: 2⁻⁴ because 2⁻⁴ = 1/16.

Question 1: Identify the mistake and correct the evaluation: 3³ ÷ 3² = 3⁵.

Answer: The exponent should be 3¹, not 3⁵, because 3³ ÷ 3² = 3³⁻² = 3¹.

Question 2: A student evaluates: (4²)² = 4⁴. Is this correct? Explain and correct if necessary.

Answer: Yes, it is correct because (a²)² = a⁴.