Question 1: Calculate the value of 5⁰.

Answer: 1

Question 2: Evaluate 10⁰ × 3⁰.

Answer: 1

Question 3: Simplify the expression (2x)⁰.

Answer: 1

Question 4: If a ≠ 0, what is the value of a⁰? Explain your reasoning.

Answer: A non-zero number raised to the zero power equals 1, based on the properties of exponents and the pattern observed when dividing powers with the same base.

Question 5: Construct a diagram on the grid that shows the exponential pattern for aⁿ with n=0, 1, 2, 3, using different values of a (e.g., 2, 3).

Answer: Student constructs a simple exponential table showing a⁰=1, a¹=a, a²=a×a, a³=a×a×a

Question 6: Plot the graph of y=2ˣ for x from -2 to 2 on the grid.

Answer: Students plot points at x=-2, -1, 0, 1, 2 with corresponding y-values 0.25, 0.5, 1, 2, 4

Question 7: Explain why any non-zero number raised to the zero power equals 1, using the properties of exponents.

Answer: Because dividing powers with the same base subtracts exponents, and aᵐ/aᵐ=1, so a⁰=1 to keep the pattern consistent.

Question 8: Identify the mistake in the following statement: 7⁰=7. Correct it and explain.

Answer: The mistake is that 7⁰=1, not 7. The zero exponent rule states any non-zero number raised to the zero power equals one.

Question 9: Calculate the value of (3⁰) + (4⁰).

Answer: 2

Question 10: A polynomial p(x) contains a term x⁰. What is the value of this term for any x? Justify your answer.

Answer: The term x⁰ equals 1 for any x ≠ 0, so it is a constant term in the polynomial.

Question 11: Challenge: Find all solutions for a in the equation a⁰=1, given that a ≠ 0.

Answer: All non-zero values of a satisfy a⁰=1.

Question 12: Describe a real-world scenario where understanding that a⁰=1 is essential.

Answer: In calculating compound interest or scaling factors, recognizing that any quantity raised to the zero power equals one helps in normalizing or simplifying models.