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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 198 · 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.What is the value of 2⁻⁷ (as a fraction)? =
  2. 2.What is the value of 5⁻² (as a fraction)? =
  3. 3.What is the value of 5⁵ × 5⁻¹? =
  4. 4.What is the value of 3¹ × 3⁻⁵? =
  5. 5.What is the value of 5⁶ × 5⁻³? =
  6. 6.What is the value of 2² × 2⁻⁶? =
  7. 7.9.3 × 10² =
  8. 8.1.2 × 10³ =
  9. 9.What is the value of 8⁵? =
  10. 10.Write 9¹² ÷ 9⁷ as a single power 9ⁿ. What is n?
  11. 11.Write 6.1 × 10⁻² as a decimal. =
  12. 12.What is the value of 4⁵? =
  13. 13.What is the value of 3⁻⁴ (as a fraction)? =
  14. 14.Write 6¹⁷ ÷ 6⁸ as a single power 6ⁿ. What is n?
  15. 15.Write 8.8 × 10⁻³ as a decimal. =
  16. 16.Write 7² × 7⁴ as a single power 7ⁿ. What is n?
  17. 17.What is the value of 2⁻² (as a fraction)? =
  18. 18.Write 6⁹ × 6⁹ as a single power 6ⁿ. What is n?
  19. 19.What is the value of 2¹³? =
  20. 20.Write 44,000 in standard form as 4.4 × 10ⁿ. What is n?
  21. 21.2.2 × 10⁵ =
  22. 22.What is the value of 4²? =
  23. 23.Write 9.5 × 10⁻³ as a decimal. =
  24. 24.What is the value of 10⁴? =
  25. 25.Write 770 in standard form as 7.7 × 10ⁿ. What is n?
  26. 26.Write 7.7 × 10⁻² as a decimal. =
  27. 27.What is the value of 6²? =
  28. 28.Write 8.3 × 10⁻⁴ as a decimal. =
  29. 29.Write 8.1 × 10⁻¹ as a decimal. =
  30. 30.What is the value of (5/6)⁻²? =
  31. 31.Write 9.7 × 10⁻³ as a decimal. =
  32. 32.Write 9¹⁸ ÷ 9⁹ as a single power 9ⁿ. What is n?
  33. 33.Write 2⁷ ÷ 2³ as a single power 2ⁿ. What is n?
  34. 34.What is the value of (6/7)⁻²? =
  35. 35.Write 7.3 × 10⁻³ as a decimal. =
  36. 36.What is the value of 2⁵ × 2⁻¹? =
  37. 37.Write 9.9 × 10⁻² as a decimal. =
  38. 38.What is the value of 2⁴ × 2⁻¹? =
  39. 39.Write (6⁹)⁷ as a single power 6ⁿ. What is n?
  40. 40.What is the value of 5⁴? =

Answer key

  1. 1/128
  2. 1/25
  3. 625
  4. 1/81
  5. 125
  6. 1/16
  7. 930
  8. 1200
  9. 32768
  10. 5
  11. 0.061
  12. 1024
  13. 1/81
  14. 9
  15. 0.0088
  16. 6
  17. 1/4
  18. 18
  19. 8192
  20. 4
  21. 220000
  22. 16
  23. 0.0095
  24. 10000
  25. 2
  26. 0.077
  27. 36
  28. 0.00083
  29. 0.81
  30. 36/25
  31. 0.0097
  32. 9
  33. 4
  34. 49/36
  35. 0.0073
  36. 16
  37. 0.099
  38. 8
  39. 63
  40. 625

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