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Cubes and Higher Powers

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Cubes and Higher Powers

Mathematical cubes and powers illustration

📚 Part 1: Understanding Cubes and Powers

Key Information:

• A cube number is when you multiply a number by itself three times: n³ = n × n × n

• Higher powers follow the same pattern: n⁴ = n × n × n × n

• The small number is called the index or power

• Remember: n¹ = n, n² = n × n (square), n³ = n × n × n (cube)

1. What does 2³ mean in words?

2 + 2 + 2

2 × 2 × 2

2 × 3

3 × 3

2. Which of these are cube numbers? (Tick all that apply)

8

16

27

64

3. Calculate 3³
4. Calculate 5³
5. What is 2⁴? Show your working.
6. Write 4 × 4 × 4 × 4 × 4 using index notation.
7. What is the value of 1³?
8. Calculate 2³ + 1³

🔢 Part 2: Higher Powers and Problem Solving

9. Calculate 3⁴ (show your working)
10. Which is larger: 2⁵ or 3³? Show your calculations.
11. A cube has sides of length 4cm. What is its volume? (Volume = length³)
12. If n³ = 125, what is the value of n?
13. Complete the pattern: 1³ = 1, 2³ = 8, 3³ = 27, 4³ = _____, 5³ = _____
14. Calculate 2⁶
15. What is 10³?
16. A bacteria colony doubles every hour. If it starts with 2 bacteria, how many will there be after 6 hours? (Write as a power, then calculate)

🧮 Part 3: Advanced Applications

17. Compare 4² and 2⁴. Which is larger?
18. If a cube has volume 216 cm³, what is the length of each side?
19. Calculate 1⁴ + 2⁴ + 3⁴
20. What is 3⁵?
21. Which of these equals 64? (Circle all correct answers)

2⁶

6⁴

22. A square has area 49 cm². A cube has the same side length. What is the cube's volume?
23. Calculate 5² × 5¹
24. What is the next term in this sequence: 2¹, 2², 2³, 2⁴, ____?

🎯 Part 4: Challenge Questions

25. If 2ⁿ = 32, what is the value of n?
26. Calculate (2³)²
27. A storage container is shaped like a cube with sides of 1.5m. How many litres can it hold? (1m³ = 1000 litres)
28. Which is the odd one out and why: 8, 27, 32, 64, 125?
29. Express 128 as a power of 2.
30. Explain in your own words the difference between 4² and 4³. Give examples.
31. A computer stores data in powers of 2. If 1 kilobyte = 2¹⁰ bytes, how many bytes are in 1 kilobyte?
32. Create your own word problem involving cube numbers.

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