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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 830 · 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 2⁹? =
  2. 2.Write 3⁹ ÷ 3⁵ as a single power 3ⁿ. What is n?
  3. 3.Write 8² × 8⁵ as a single power 8ⁿ. What is n?
  4. 4.What is the value of 10² × 10⁻⁶? =
  5. 5.What is the value of 4⁶? =
  6. 6.What is the value of (2/5)⁻¹? =
  7. 7.Write 6⁵ × 6⁷ as a single power 6ⁿ. What is n?
  8. 8.Write 1.8 × 10⁻⁴ as a decimal. =
  9. 9.Write 5.6 × 10⁻³ as a decimal. =
  10. 10.What is the value of 3²? =
  11. 11.What is the value of 10¹ × 10⁻²? =
  12. 12.Write 3¹³ ÷ 3⁷ as a single power 3ⁿ. What is n?
  13. 13.Write 2¹¹ ÷ 2³ as a single power 2ⁿ. What is n?
  14. 14.What is the value of 8⁴? =
  15. 15.Write 2³ × 2² as a single power 2ⁿ. What is n?
  16. 16.Write (7²)² as a single power 7ⁿ. What is n?
  17. 17.What is the value of 2⁶ × 2⁻²? =
  18. 18.What is the value of 5⁴? =
  19. 19.What is the value of 3⁸? =
  20. 20.What is the value of 8²? =
  21. 21.Write 4.5 × 10⁻⁴ as a decimal. =
  22. 22.Write 51,00,000 in standard form as 5.1 × 10ⁿ. What is n?
  23. 23.What is the value of 5¹ × 5⁻⁶? =
  24. 24.Write 7.5 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 2³? =
  26. 26.What is the value of 10⁵ × 10⁻²? =
  27. 27.What is the value of 2⁻² (as a fraction)? =
  28. 28.What is the value of (4/5)⁻²? =
  29. 29.What is the value of 3² × 3⁻¹? =
  30. 30.Write 2,10,00,000 in standard form as 2.1 × 10ⁿ. What is n?
  31. 31.What is the value of 2⁻⁸ (as a fraction)? =
  32. 32.Write 1,700 in standard form as 1.7 × 10ⁿ. What is n?
  33. 33.What is the value of 7⁴? =
  34. 34.Write 8¹² ÷ 8⁹ as a single power 8ⁿ. What is n?
  35. 35.Write 7⁴ × 7⁸ as a single power 7ⁿ. What is n?
  36. 36.Write 4⁶ × 4⁶ as a single power 4ⁿ. What is n?
  37. 37.What is the value of 10⁶ × 10⁻²? =
  38. 38.What is the value of 2²? =
  39. 39.6.5 × 10⁶ =
  40. 40.What is the value of 7²? =

Answer key

  1. 512
  2. 4
  3. 7
  4. 1/10000
  5. 4096
  6. 5/2
  7. 12
  8. 0.00018
  9. 0.0056
  10. 9
  11. 1/10
  12. 6
  13. 8
  14. 4096
  15. 5
  16. 4
  17. 16
  18. 625
  19. 6561
  20. 64
  21. 0.00045
  22. 6
  23. 1/3125
  24. 0.75
  25. 8
  26. 1000
  27. 1/4
  28. 25/16
  29. 3
  30. 7
  31. 1/256
  32. 3
  33. 2401
  34. 3
  35. 12
  36. 12
  37. 10000
  38. 4
  39. 6500000
  40. 49

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