📚 Part 1: Understanding Indices

1. What does 2⁻³ equal?

-8

1/8

-1/8

8

2. Which of the following are equivalent to 5⁻²? (Tick all that apply)

1/25

-25

1/5²

0.04

3. Simplify: 3² × 3⁻⁵

3⁻³

3⁷

3⁻¹⁰

9⁻³

4. What is the value of 4⁰?

0

1

4

Undefined

✏️ Part 2: Calculations and Simplification

5. Calculate the exact value of 2⁻⁴

6. Simplify the following expressions:

a) 6³ × 6⁻⁷ = ___________

b) (4⁻²)³ = ___________

c) 10⁻³ × 10⁵ = ___________

d) 7⁻¹ ÷ 7⁻⁴ = ___________

7. Express as a single power:

a) 1/8² = 8_____

b) 1/(3⁵) = 3_____

c) 1/x³ = x_____

8. Show your working to calculate: 5⁻² + 3⁻¹

🎯 Part 3: Problem Solving and Reasoning

9. A bacteria population decreases according to the formula P = 1000 × 2⁻ᵗ, where t is time in hours. What is the population after 3 hours?

10. Explain in your own words what a negative index means and why 3⁻² = 1/3².

11. Challenge: If 2ˣ = 1/16, what is the value of x? Show your reasoning.

12. Reflection: How does understanding negative indices help you see the order and patterns in mathematics that reflect God's creation?

Positive and Negative Indices

Positive and Negative Indices

📚 Part 1: Understanding Indices

✏️ Part 2: Calculations and Simplification

🎯 Part 3: Problem Solving and Reasoning

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