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Positive and Negative Indices
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Positive and Negative Indices
📚 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?
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