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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 219 · 40 sums
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The method (Same base, work the powers): aᵐ × aⁿ = aᵐ⁺ⁿ, aᵐ ÷ aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1. a⁻ⁿ = 1/aⁿ, and (a/b)⁻ⁿ = (b/a)ⁿ. Standard form: one digit before the point × a power of 10 — 4500000 = 4.5 × 10⁶. × 10⁻ⁿ moves the decimal point n places to the left: 2.5 × 10⁻³ = 0.0025.

NameDateTime takenScore ___ / 40
  1. 1.Write 2 × 10⁻¹ as a decimal. =
  2. 2.What is the value of 10⁶ × 10⁻³? =
  3. 3.Write 4.1 × 10⁻¹ as a decimal. =
  4. 4.What is the value of 2¹¹? =
  5. 5.Write 400 in standard form as 4 × 10ⁿ. What is n?
  6. 6.Write 5¹⁴ ÷ 5⁷ as a single power 5ⁿ. What is n?
  7. 7.Write 130 in standard form as 1.3 × 10ⁿ. What is n?
  8. 8.What is the value of (3/4)⁻¹? =
  9. 9.Write 6.1 × 10⁻² as a decimal. =
  10. 10.What is the value of 2¹²? =
  11. 11.What is the value of 5²? =
  12. 12.Write (8⁶)⁵ as a single power 8ⁿ. What is n?
  13. 13.What is the value of 5² × 5⁻⁵? =
  14. 14.What is the value of 5² × 5⁻³? =
  15. 15.What is the value of (3/8)⁻¹? =
  16. 16.Write 8 × 10⁻⁴ as a decimal. =
  17. 17.Write 3⁴ ÷ 3² as a single power 3ⁿ. What is n?
  18. 18.Write 2⁷ ÷ 2³ as a single power 2ⁿ. What is n?
  19. 19.What is the value of 2¹⁴? =
  20. 20.Write 4 × 10⁻³ as a decimal. =
  21. 21.Write 4.7 × 10⁻¹ as a decimal. =
  22. 22.What is the value of 7⁻¹ (as a fraction)? =
  23. 23.What is the value of 3⁻⁴ (as a fraction)? =
  24. 24.What is the value of (2/9)⁻¹? =
  25. 25.Write 3.7 × 10⁻⁴ as a decimal. =
  26. 26.What is the value of 9⁻² (as a fraction)? =
  27. 27.Write 5.6 × 10⁻¹ as a decimal. =
  28. 28.Write (7⁷)⁶ as a single power 7ⁿ. What is n?
  29. 29.Write 9,200 in standard form as 9.2 × 10ⁿ. What is n?
  30. 30.What is the value of 3⁶ × 3⁻³? =
  31. 31.What is the value of 2⁶ × 2⁻⁶? =
  32. 32.What is the value of 8³? =
  33. 33.What is the value of 3⁹? =
  34. 34.What is the value of 10¹ × 10⁻⁶? =
  35. 35.What is the value of 8⁻¹ (as a fraction)? =
  36. 36.Write 12,000 in standard form as 1.2 × 10ⁿ. What is n?
  37. 37.What is the value of 9⁴? =
  38. 38.Write 2.7 × 10⁻¹ as a decimal. =
  39. 39.Write (2⁶)⁴ as a single power 2ⁿ. What is n?
  40. 40.8.4 × 10³ =

Answer key

  1. 0.2
  2. 1000
  3. 0.41
  4. 2048
  5. 2
  6. 7
  7. 2
  8. 4/3
  9. 0.061
  10. 4096
  11. 25
  12. 30
  13. 1/125
  14. 1/5
  15. 8/3
  16. 0.0008
  17. 2
  18. 4
  19. 16384
  20. 0.004
  21. 0.47
  22. 1/7
  23. 1/81
  24. 9/2
  25. 0.00037
  26. 1/81
  27. 0.56
  28. 42
  29. 3
  30. 27
  31. 1
  32. 512
  33. 19683
  34. 1/100000
  35. 1/8
  36. 4
  37. 6561
  38. 0.27
  39. 24
  40. 8400

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