Question 1: Simplify the expression: 8^(2/3).

Answer: 4

Question 2: Calculate the value of a^(3/4) when a = 16.

Answer: 2

Question 3: Express 81^(1/4) as a simplified radical.

Answer: 3

Question 4: Calculate (27)^(2/3).

Answer: 9

Question 5: Evaluate the expression: (125)^(3/5).

Answer: 25

Question 6: A bottle contains a liquid volume proportional to 125^(1/3). If the volume is 5 units, what is the volume in terms of the cube root?

Answer: The volume is proportional to 5 units, since 125^(1/3) = 5.

Question 7: Simplify: (16)^(3/4).

Answer: 8

Question 8: Construct a triangle with side lengths corresponding to the values of 64^(1/6), 81^(1/4), and 125^(1/3).

Answer: Sides are 2, 3, and 5 respectively; students will draw accordingly.

Question 9: Calculate the value of a^(m/n) where a=32, m=5, n=5.

Answer: 2

Question 10: Identify the mistake in simplifying the expression: 64^(1/3) = 4.

Answer: Incorrect because 64^(1/3) = 4 is wrong; 64^(1/3)=4 is false; correct answer is 4, but the mistake is in the calculation. Students should recognize 64^(1/3)= 4, which is correct. The mistake would be if they said 64^(1/3)=8 or similar.

Question 11: Evaluate: (32)^(2/5).

Answer: 4