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Index Laws Practice
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Index Laws Practice
🔢 Part 1: Understanding Indices
1. What does 4³ mean as repeated multiplication?
4 + 4 + 4
4 × 4 × 4
4 × 3
3 × 3 × 3 × 3
2. Calculate: 2³ × 2⁴
2⁷
2¹²
4⁷
8⁴
3. Simplify: 5⁶ ÷ 5²
5³
5⁴
5⁸
1¹²
4. Which expressions equal 3⁵? (Check all that apply)
3² × 3³
3⁷ ÷ 3²
3 × 3 × 3 × 3 × 3
3¹⁰ ÷ 3⁵
📝 Part 2: Apply the Index Laws
5. Complete the pattern by filling in the blanks:
a) 7² × 7³ = 7____
b) 6⁸ ÷ 6⁵ = 6____
c) 4¹ × 4____ = 4⁶
d) 9⁷ ÷ 9____ = 9³
6. Show your working to simplify these expressions:
a) 8³ × 8⁴
b) 10⁹ ÷ 10⁶
7. Real-world application: A square has side length 3 metres. If you create a cube with the same side length, write the volume using indices.
Volume = _______ cubic metres
8. Explain in your own words what happens to the indices when you multiply powers with the same base:
🚀 Part 3: Challenge Questions
9. Extension: If 2ˣ × 2³ = 2⁸, what is the value of x?
x = _______
10. Create your own index law problem and solve it:
Problem: ________________________________
11. Looking ahead: What do you think 5⁰ might equal? Give a reason for your answer.
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