Question 1: Calculate 5⁰.

Answer: 1

Question 2: Evaluate the expression: (3/4)⁰.

Answer: 1

Question 3: What is the value of 10⁰?

Answer: 1

Question 4: Simplify: (2²) ÷ (2²).

Answer: 1

Question 1: Explain why any non-zero number raised to the zero power equals 1. Provide an example with 7.

Answer: Any number a ≠ 0, a⁰ = 1 because of the laws of exponents, as shown by (a¹)/(a¹) = a⁰, and since a¹/a¹ = 1, it follows that a⁰ = 1.

Question 2: Given that 4³ = 64 and 4² = 16, find the value of 4⁰ using the laws of exponents.

Answer: 1

Question 3: If a⁰ = 1, what is the value of a⁻² in terms of a?

Answer: a⁻² = 1/a²

Question 4: If 2ˣ = 1, what is the value of x?

Answer: x = 0

Question 1: A scientist models a process with the equation N = N₀ × a⁰, where N₀ is initial quantity and a ≠ 0. If a⁰ = 1, what does this tell us about the quantity N?

Answer: It indicates that the quantity N remains equal to N₀ when the exponent is zero, confirming that any non-zero base raised to zero is 1, so N = N₀.

Question 2: A calculator displays 1 after computing 3⁰. Explain why this is consistent with exponent rules.

Answer: Because the rule a⁰ = 1 applies to all non-zero a, including 3, so 3⁰ = 1, which is correctly displayed.

Question 1: Prove that (a/b)⁰ = 1 for any non-zero a and b, using the laws of exponents.

Answer: Because (a/b)⁰ = (a/b)⁰ = 1 by the law a⁰=1, regardless of the base.

Question 2: If a ≠ 0 and a¹ = a, what is a⁻¹? Demonstrate the reasoning.

Answer: a⁻¹ = 1/a, because the rule a⁻¹ = 1/a follows from a¹/a¹ = a⁰ = 1.

Question 1: Identify and correct the error in this statement: 7⁰ = 7.

Answer: The error is that 7⁰ = 1, not 7. The zero exponent rule states a⁰ = 1 for any a ≠ 0.

Question 2: Compare the values of 1⁰ and 0⁰. Are they both defined? Explain.

Answer: 1⁰ = 1 by the rule. 0⁰ is undefined in some contexts due to indeterminate forms, but in pure algebra, 0⁰ is often defined as 1 for consistency.