Question 1: Evaluate the expression: 5^0

Answer: 1

Question 2: Simplify: (3^4) ÷ (3^4)

Answer: 1

Question 3: Explain why any non-zero number raised to the zero power equals 1. Provide a brief proof.

Answer: Because of the laws of exponents: a^m ÷ a^m = a^{m-m} = a^0, which simplifies to 1 for any a ≠ 0.

Question 4: Calculate: (2^5) ÷ (2^2)

Answer: 8

Question 5: Plot the graph of y=2x for x from -3 to 3.

Answer: Students draw points corresponding to y=2x on the grid.

Question 6: Construct a triangle with side lengths 3, 4, and 5. Verify if it is a right-angled triangle.

Answer: Yes, because 3^2 + 4^2 = 5^2 (9 + 16 = 25).

Question 7: If a^0 = 1, what is 0^0? Provide reasoning for your answer.

Answer: 0^0 is indeterminate or undefined in some contexts, but by the zero exponent rule, it is often defined as 1 for consistency in algebra.

Question 8: Identify and correct the mistake: 7^0 = 0.

Answer: The mistake is assuming 7^0 = 0. The correct value is 1 because any non-zero number to the zero power equals 1.

Question 9: Prove that for any non-zero number a, a^0 = 1, using properties of exponents.

Answer: Using the property a^m / a^m = a^{m-m} = a^0, and since a^m / a^m = 1, it follows that a^0 = 1.

Question 10: Solve for x: 2^x = 1

Answer: 0

Question 11: Explain how the zero index rule helps simplify expressions in algebra.

Answer: It allows us to reduce powers with the same base by subtracting exponents, knowing that any base (except zero) raised to zero equals 1, simplifying complex calculations.