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Negative Exponents Exploration

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Negative Exponents Exploration

Mathematical symbols and exponents illustration

🎯 WALT: Understand how repeated division leads to negative exponents

1. Look at this pattern. What comes next?

10³ = 1000, 10² = 100, 10¹ = 10, 10⁰ = 1, _______ = 0.1

10⁻¹

10¹

10⁻⁰

10⁻²

2. Which of these expressions are equal to 1/100? (Tick all that apply)

10⁻²

0.01

1 ÷ 10²

10²

3. What does 2⁻³ equal?

1/8

-8

1/6

8

4. Complete this rule: a⁻ⁿ = _________

-aⁿ

1/aⁿ

a × n

n/a

✏️ Working with Negative Exponents

5. Calculate these negative exponents. Show your working.

a) 5⁻² = ____________

b) 3⁻¹ = ____________

c) 4⁻³ = ____________

6. Write these repeated divisions as negative exponents:

a) 1 ÷ 6 ÷ 6 ÷ 6 = ____________

b) 1/(2 × 2 × 2 × 2) = ____________

c) 1 ÷ 7² = ____________

7. Explain in your own words what a negative exponent means:

🌟 Real-World Applications

8. A bacteria sample shrinks to 1/10 of its size every hour. After 3 hours, it will be _______ of its original size.

10⁻³

3⁻¹⁰

10³

1/30

9. Extension Challenge: In scientific notation, very small numbers use negative exponents. Write 0.0005 in scientific notation:

0.0005 = _______ × 10_____

10. Create your own example of where negative exponents might be useful in real life:

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