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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 979 · 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 9,100 in standard form as 9.1 × 10ⁿ. What is n?
  2. 2.Write 9 × 10⁻¹ as a decimal. =
  3. 3.Write 7.9 × 10⁻¹ as a decimal. =
  4. 4.Write 5.3 × 10⁻¹ as a decimal. =
  5. 5.Write 67,000 in standard form as 6.7 × 10ⁿ. What is n?
  6. 6.What is the value of 5⁵? =
  7. 7.What is the value of 3¹ × 3⁻⁶? =
  8. 8.What is the value of 10⁵ × 10⁻⁴? =
  9. 9.Write 5 × 10⁻⁴ as a decimal. =
  10. 10.4.6 × 10⁷ =
  11. 11.What is the value of 5³ × 5⁻⁵? =
  12. 12.What is the value of (4/7)⁻²? =
  13. 13.What is the value of 4⁷? =
  14. 14.What is the value of 4³? =
  15. 15.Write 3³ × 3² as a single power 3ⁿ. What is n?
  16. 16.Write 2 × 10⁻¹ as a decimal. =
  17. 17.What is the value of 2⁷? =
  18. 18.Write 3.4 × 10⁻³ as a decimal. =
  19. 19.Write 1.5 × 10⁻⁴ as a decimal. =
  20. 20.What is the value of 7⁻³ (as a fraction)? =
  21. 21.What is the value of 5³ × 5⁻¹? =
  22. 22.Write (8³)⁵ as a single power 8ⁿ. What is n?
  23. 23.3.2 × 10⁴ =
  24. 24.What is the value of 2⁵ × 2⁻⁶? =
  25. 25.Write (4³)⁸ as a single power 4ⁿ. What is n?
  26. 26.Write 5.9 × 10⁻² as a decimal. =
  27. 27.What is the value of 10⁻² (as a fraction)? =
  28. 28.What is the value of (3/7)⁻¹? =
  29. 29.Write (5²)⁷ as a single power 5ⁿ. What is n?
  30. 30.What is the value of 2²? =
  31. 31.Write 8⁵ × 8⁵ as a single power 8ⁿ. What is n?
  32. 32.Write (5³)⁹ as a single power 5ⁿ. What is n?
  33. 33.What is the value of 5⁻⁴ (as a fraction)? =
  34. 34.Write (2⁴)³ as a single power 2ⁿ. What is n?
  35. 35.Write 3² × 3³ as a single power 3ⁿ. What is n?
  36. 36.Write 22,000 in standard form as 2.2 × 10ⁿ. What is n?
  37. 37.Write (9⁸)³ as a single power 9ⁿ. What is n?
  38. 38.Write (3⁹)⁸ as a single power 3ⁿ. What is n?
  39. 39.Write 2.9 × 10⁻² as a decimal. =
  40. 40.What is the value of 3⁶ × 3⁻⁶? =

Answer key

  1. 3
  2. 0.9
  3. 0.79
  4. 0.53
  5. 4
  6. 3125
  7. 1/243
  8. 10
  9. 0.0005
  10. 46000000
  11. 1/25
  12. 49/16
  13. 16384
  14. 64
  15. 5
  16. 0.2
  17. 128
  18. 0.0034
  19. 0.00015
  20. 1/343
  21. 25
  22. 15
  23. 32000
  24. 1/2
  25. 24
  26. 0.059
  27. 1/100
  28. 7/3
  29. 14
  30. 4
  31. 10
  32. 27
  33. 1/625
  34. 12
  35. 5
  36. 4
  37. 24
  38. 72
  39. 0.029
  40. 1

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