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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 922 · 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 8¹² ÷ 8³ as a single power 8ⁿ. What is n?
  2. 2.What is the value of 3⁻¹ (as a fraction)? =
  3. 3.What is the value of 2⁻⁶ (as a fraction)? =
  4. 4.Write 3⁵ × 3⁶ as a single power 3ⁿ. What is n?
  5. 5.Write (3⁸)³ as a single power 3ⁿ. What is n?
  6. 6.Write 7² × 7⁶ as a single power 7ⁿ. What is n?
  7. 7.What is the value of 5⁵? =
  8. 8.What is the value of 10² × 10⁻⁶? =
  9. 9.Write 1.6 × 10⁻¹ as a decimal. =
  10. 10.Write 8 × 10⁻² as a decimal. =
  11. 11.3.6 × 10⁴ =
  12. 12.What is the value of 2⁴ × 2⁻²? =
  13. 13.What is the value of 9²? =
  14. 14.Write 5,500 in standard form as 5.5 × 10ⁿ. What is n?
  15. 15.Write 3⁹ × 3⁵ as a single power 3ⁿ. What is n?
  16. 16.What is the value of 3⁵ × 3⁻⁶? =
  17. 17.Write 6.6 × 10⁻³ as a decimal. =
  18. 18.What is the value of (4/5)⁻²? =
  19. 19.Write 4.8 × 10⁻² as a decimal. =
  20. 20.Write (4⁵)⁴ as a single power 4ⁿ. What is n?
  21. 21.Write 4⁹ × 4³ as a single power 4ⁿ. What is n?
  22. 22.Write 6.8 × 10⁻¹ as a decimal. =
  23. 23.Write 3 × 10⁻⁴ as a decimal. =
  24. 24.Write 2.9 × 10⁻³ as a decimal. =
  25. 25.What is the value of 5³ × 5⁻²? =
  26. 26.What is the value of 6⁵? =
  27. 27.What is the value of 5³ × 5⁻⁶? =
  28. 28.What is the value of (1/9)⁻¹? =
  29. 29.7 × 10⁶ =
  30. 30.Write 1.3 × 10⁻² as a decimal. =
  31. 31.What is the value of 2⁶? =
  32. 32.What is the value of 2¹ × 2⁻⁶? =
  33. 33.Write 4.7 × 10⁻³ as a decimal. =
  34. 34.Write 7⁵ × 7³ as a single power 7ⁿ. What is n?
  35. 35.Write 1,600 in standard form as 1.6 × 10ⁿ. What is n?
  36. 36.What is the value of 2⁷? =
  37. 37.Write 8² × 8³ as a single power 8ⁿ. What is n?
  38. 38.Write 8.8 × 10⁻¹ as a decimal. =
  39. 39.What is the value of 2¹¹? =
  40. 40.3.8 × 10² =

Answer key

  1. 9
  2. 1/3
  3. 1/64
  4. 11
  5. 24
  6. 8
  7. 3125
  8. 1/10000
  9. 0.16
  10. 0.08
  11. 36000
  12. 4
  13. 81
  14. 3
  15. 14
  16. 1/3
  17. 0.0066
  18. 25/16
  19. 0.048
  20. 20
  21. 12
  22. 0.68
  23. 0.0003
  24. 0.0029
  25. 5
  26. 7776
  27. 1/125
  28. 9
  29. 7000000
  30. 0.013
  31. 64
  32. 1/32
  33. 0.0047
  34. 8
  35. 3
  36. 128
  37. 5
  38. 0.88
  39. 2048
  40. 380

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