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Cubes and Higher Powers

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Cubes and Higher Powers

Mathematical powers and cubes illustration

📚 Understanding Powers and Cubes

Key Information:

• A power tells us how many times to multiply a number by itself

• 2³ = 2 × 2 × 2 = 8 (read as "2 cubed" or "2 to the power of 3")

• 3⁴ = 3 × 3 × 3 × 3 = 81 (read as "3 to the power of 4")

• The small number is called the index or power

1. Complete these definitions:

a) 5³ means multiply 5 by itself _______ times

b) In the expression 4², the number 4 is called the _______ and 2 is called the _______

2. Write these in expanded form (don't calculate yet):

a) 3³ = _____ × _____ × _____

b) 2⁴ = _____ × _____ × _____ × _____

c) 6² = _____ × _____

3. Calculate these cube numbers:

a) 1³ = _____

b) 2³ = _____

c) 3³ = _____

d) 4³ = _____

e) 5³ = _____

4. Calculate these fourth powers:

a) 2⁴ = _____

b) 3⁴ = _____

c) 1⁴ = _____

🔢 Working with Higher Powers

5. Multiple choice - Which expression equals 64?

2⁶

All of the above

6. Calculate these powers (show your working):

a) 6² = _____

b) 7² = _____

c) 8² = _____

d) 9² = _____

e) 10² = _____

7. Find the value of:

a) 2⁵ = _____

b) 3⁵ = _____

c) 10³ = _____

d) 10⁴ = _____

8. Which is larger? Circle your answer and explain why:

a) 3⁴ or 4³? ________________

b) 2⁶ or 6²? ________________

🎯 Problem Solving with Powers

9. A cube has sides of length 7cm. What is its volume?

Volume = _______ cm³

10. Complete the pattern:

10¹ = 10

10² = 100

10³ = _____

10⁴ = _____

10⁵ = _____

Describe the pattern: ________________________________________________

11. Challenge: If 2ⁿ = 32, what is the value of n?

n = _____

12. Real-life problem: A bacteria culture doubles every hour. If you start with 2 bacteria, how many will there be after 4 hours?

Write as a power: _____________

Calculate: _______ bacteria

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