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Negative Indices Exploration

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Negative Indices Exploration

Mathematical expressions with negative indices

📚 Part 1: Understanding Negative Indices

1. What does 2⁻³ mean?

-2 × -2 × -2

1/(2 × 2 × 2)

2 × 2 × 2

-8

2. Which of these expressions are equal to 5⁻²? (Select all that apply)

1/25

1/5²

(1/5)²

-25

3. Calculate 3⁻² =

Show your working: ____________________

Answer: ____________________

4. Complete the pattern:

4³ = 64

4² = 16

4¹ = 4

4⁰ = ____

4⁻¹ = ____

4⁻² = ____

✏️ Part 2: Converting and Calculating

5. Convert these expressions with negative indices to fraction form:

a) 7⁻¹ = ____________________

b) 2⁻⁴ = ____________________

c) 10⁻³ = ____________________

6. Calculate the value of each expression:

a) 6⁻² = ____________________

b) 2⁻⁵ = ____________________

c) 5⁻¹ = ____________________

7. A radioactive substance decays according to the formula: Amount = 100 × 2⁻ᵗ grams, where t is time in hours.

Calculate the amount remaining after:

a) 1 hour: ____________________

b) 3 hours: ____________________

c) Explain what happens to the amount over time:

🧠 Part 3: Real-World Applications

8. A cup of coffee cools according to the temperature formula: T = 80 × 3⁻ᵗ/¹⁰ °C, where t is time in minutes.

What is the temperature after 10 minutes?

9. Explain in your own words what a negative index means and give an example:
10. Extension Challenge: If 8⁻¹ × 8ˣ = 8², what is the value of x?

Show your reasoning:

x = ____________________

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