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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 982 · 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 2³ × 2⁻⁶? =
  2. 2.8.4 × 10⁶ =
  3. 3.Write 3.7 × 10⁻² as a decimal. =
  4. 4.What is the value of 2⁻³ (as a fraction)? =
  5. 5.What is the value of (3/4)⁻¹? =
  6. 6.4.8 × 10³ =
  7. 7.What is the value of 9³? =
  8. 8.Write 54,000 in standard form as 5.4 × 10ⁿ. What is n?
  9. 9.What is the value of 5² × 5⁻⁶? =
  10. 10.Write 2.1 × 10⁻³ as a decimal. =
  11. 11.What is the value of 6⁶? =
  12. 12.What is the value of 2¹ × 2⁻¹? =
  13. 13.What is the value of 6³? =
  14. 14.What is the value of 2² × 2⁻⁵? =
  15. 15.8.4 × 10² =
  16. 16.Write 7.7 × 10⁻⁴ as a decimal. =
  17. 17.Write (4⁷)⁸ as a single power 4ⁿ. What is n?
  18. 18.What is the value of 5²? =
  19. 19.What is the value of 10¹ × 10⁻⁴? =
  20. 20.Write 7.5 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 5⁻⁴ (as a fraction)? =
  22. 22.Write 8⁹ × 8⁷ as a single power 8ⁿ. What is n?
  23. 23.Write 9.9 × 10⁻³ as a decimal. =
  24. 24.What is the value of (2/7)⁻¹? =
  25. 25.What is the value of 2⁴ × 2⁻¹? =
  26. 26.What is the value of 2² × 2⁻¹? =
  27. 27.Write 7⁷ × 7³ as a single power 7ⁿ. What is n?
  28. 28.What is the value of 5⁶ × 5⁻⁵? =
  29. 29.Write 8,80,000 in standard form as 8.8 × 10ⁿ. What is n?
  30. 30.What is the value of 2¹⁰? =
  31. 31.Write 63,000 in standard form as 6.3 × 10ⁿ. What is n?
  32. 32.What is the value of 2¹ × 2⁻³? =
  33. 33.What is the value of 6⁻³ (as a fraction)? =
  34. 34.What is the value of 5⁵ × 5⁻⁴? =
  35. 35.Write (7²)³ as a single power 7ⁿ. What is n?
  36. 36.2.5 × 10² =
  37. 37.What is the value of (1/9)⁻¹? =
  38. 38.Write 8⁴ ÷ 8² as a single power 8ⁿ. What is n?
  39. 39.Write 5⁴ × 5⁴ as a single power 5ⁿ. What is n?
  40. 40.Write 6¹⁰ ÷ 6⁶ as a single power 6ⁿ. What is n?

Answer key

  1. 1/8
  2. 8400000
  3. 0.037
  4. 1/8
  5. 4/3
  6. 4800
  7. 729
  8. 4
  9. 1/625
  10. 0.0021
  11. 46656
  12. 1
  13. 216
  14. 1/8
  15. 840
  16. 0.00077
  17. 56
  18. 25
  19. 1/1000
  20. 0.75
  21. 1/625
  22. 16
  23. 0.0099
  24. 7/2
  25. 8
  26. 2
  27. 10
  28. 5
  29. 5
  30. 1024
  31. 4
  32. 1/4
  33. 1/216
  34. 5
  35. 6
  36. 250
  37. 9
  38. 2
  39. 8
  40. 4

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