Question 1: Calculate 3^4.

Answer: 81

Question 2: Evaluate 2^3 × 2^4.

Answer: 128

Question 3: Simplify (5^2)^3.

Answer: 125

Question 4: Calculate the value of 10^0.

Answer: 1

Question 5: Evaluate 4^3 ÷ 4^2.

Answer: 4

Question 6: Express 16 in index form with a base of 2.

Answer: 2^4

Question 7: Calculate (2^3)^2.

Answer: 64

Question 8: If 3^x = 27, find the value of x.

Answer: 3

Question 9: Construct a triangle with sides corresponding to the lengths 2^3, 2^4, and 2^5. Use the grid to draw the triangle.

Answer: Students draw based on grid

Question 10: A bacterial population doubles every day. If the initial population is 5 and represented as 5 × 2^n, what is the population after 6 days?

Answer: 320

Question 11: Evaluate and explain: 2^5 + 2^5.

Answer: 2 × 32 = 64

Question 12: Calculate 8^2 in index notation with base 2, and verify your result.

Answer: 2^6

Question 13: Identify and correct the mistake: Evaluate 2^3 + 2^3 as 2^4.

Answer: Incorrect because 2^3 + 2^3 = 2 × 2^3 = 2^4 only if adding same bases with multiplication, but addition is different; correct is 2^3 + 2^3 = 2 × 8 = 16

Question 14: Challenge: Simplify 2^–3 × 2^5, and explain the rules used.

Answer: 2^2