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Year 8 Maths — Powers and exponents

Read and write a power, work out its value, and use the laws for multiplying and dividing powers of the same base.

Name: ________________________

Before you start

This line runs to thirty-two in twos. Find 2, 4, 8, 16 and 32 on it, and see how far apart they get.

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Each of those is double the one before, so every jump is as long as the whole walk that came before it. A power grows far faster than the small numbers writing it suggest.

  1. 1.100000 is 10 to some power. What is that power?

  2. 2.Which is larger: 2⁵ or 5²?

    • a) They are equal
    • b) 5²
    • c) There is no way to tell
    • d) 2⁵

  3. 3.Which power means the same as 3 × 3 × 3 × 3?

    • a) 3⁵
    • b) 3⁴
    • c) 3 × 4
    • d) 4³

  4. 4.Match each number to the power of 10 it is equal to.

    • 1
    • 10
    • 100
    • 1000
    • 10000
    • 10⁰
    • 10⁴
    • 10³
    • 10²
    • 10¹

  5. 5.Work out 5⁶ ÷ 5⁴ as an ordinary number.

  6. 6.7⁴ × 7³ is the same as which single power?

    • a) 7¹²
    • b) 7¹
    • c) 49⁷
    • d) 7⁷

  7. 7.What is 6²?

  8. 8.What is 10³?

Answer key — Year 8 Maths — Powers and exponents

  1. 1. 5
  2. 2. d) 2⁵
  3. 3. b) 3⁴
  4. 4. 1 → 10⁰; 10 → 10¹; 100 → 10²; 1000 → 10³; 10000 → 10⁴
  5. 5. 25
  6. 6. d) 7⁷
  7. 7. 36
  8. 8. 1000