Question 1: Calculate the value of 5^0.

Answer: 1

Question 2: Simplify the expression: (2^3) ÷ (2^3).

Answer: 1

Question 3: Prove that any non-zero number raised to the power of zero equals 1 using the laws of exponents.

Answer: Using the law a^m ÷ a^n = a^{m-n}, set m = n to get a^n ÷ a^n = a^{n-n} = a^0. Since a^n ÷ a^n = 1, it follows that a^0 = 1.

Question 4: Construct a power expression with base 3 that equals 1 using the zero index rule.

Answer: 3^0

Question 5: Explain why any non-zero number to the zero power is equal to 1, including an example.

Answer: Because of the laws of exponents, dividing a^n by itself (a^n ÷ a^n) equals 1. Using this, for example, 7^3 ÷ 7^3 = 7^{3-3} = 7^0, and since 7^3 ÷ 7^3=1, it shows 7^0=1.

Question 6: Evaluate the expression: (10^4) × (10^0).

Answer: 10000

Question 7: If 4^x = 1, what is the value of x? Show your reasoning.

Answer: x=0, because 4^0=1

Question 8: A car's speed is constant at 60 km/hr. How many hours does it take to travel 0 km? Justify your answer.

Answer: It takes 0 hours because distance divided by speed: 0 ÷ 60 = 0.

Question 9: Plot the graph of y=2^x for x from -2 to 2 on the grid.

Answer: Students will plot points at x= -2, -1, 0, 1, 2, corresponding to y= 0.25, 0.5, 1, 2, 4 respectively.

Question 10: Construct a triangle on the grid with sides of lengths 3, 4, and 5, with the side of length 4 on the x-axis. Label the vertices clearly.

Answer: Students draw and label the triangle accordingly, confirming side lengths using grid measurements.

Question 11: Identify and correct the mistake: 'Since any number to the power of zero is zero, 8^0=0.'

Answer: The mistake is that any non-zero number to the zero power equals 1, not 0. Correct statement: 8^0=1.

Question 12: Challenge: Prove that (a^0)(b^0) = (ab)^0 for non-zero a and b using the laws of exponents.

Answer: Using the law a^m b^n = (ab)^m+n, and the fact that a^0 = 1 and b^0=1, we get (a^0)(b^0)=1×1=1, and (ab)^0=1. Thus, both sides equal 1, confirming the property.