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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 622 · 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 3⁻² (as a fraction)? =
  2. 2.What is the value of 3² × 3⁻¹? =
  3. 3.What is the value of 2² × 2⁻⁶? =
  4. 4.Write 8,70,00,000 in standard form as 8.7 × 10ⁿ. What is n?
  5. 5.What is the value of 4³? =
  6. 6.What is the value of 3¹ × 3⁻³? =
  7. 7.Write 8.3 × 10⁻² as a decimal. =
  8. 8.Write (3⁹)⁸ as a single power 3ⁿ. What is n?
  9. 9.Write 4.4 × 10⁻⁴ as a decimal. =
  10. 10.Write 4⁸ × 4⁴ as a single power 4ⁿ. What is n?
  11. 11.Write 9.8 × 10⁻⁴ as a decimal. =
  12. 12.What is the value of 6⁶? =
  13. 13.Write 3 × 10⁻⁴ as a decimal. =
  14. 14.What is the value of (2/5)⁻²? =
  15. 15.What is the value of 9⁵? =
  16. 16.What is the value of 7⁴? =
  17. 17.What is the value of (1/5)⁻¹? =
  18. 18.Write 3.3 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 2⁻⁹ (as a fraction)? =
  20. 20.What is the value of 2³ × 2⁻⁴? =
  21. 21.What is the value of (1/3)⁻²? =
  22. 22.Write (4⁷)² as a single power 4ⁿ. What is n?
  23. 23.What is the value of 3⁴? =
  24. 24.What is the value of 8⁻³ (as a fraction)? =
  25. 25.Write (9³)⁶ as a single power 9ⁿ. What is n?
  26. 26.Write 9⁶ × 9⁸ as a single power 9ⁿ. What is n?
  27. 27.What is the value of 4²? =
  28. 28.What is the value of 2¹ × 2⁻¹? =
  29. 29.What is the value of 2³? =
  30. 30.What is the value of (4/9)⁻¹? =
  31. 31.What is the value of 2¹²? =
  32. 32.What is the value of 10⁻¹ (as a fraction)? =
  33. 33.What is the value of 10¹ × 10⁻³? =
  34. 34.Write 6⁸ ÷ 6⁴ as a single power 6ⁿ. What is n?
  35. 35.Write 4.3 × 10⁻² as a decimal. =
  36. 36.Write 7¹⁷ ÷ 7⁸ as a single power 7ⁿ. What is n?
  37. 37.What is the value of 2⁹? =
  38. 38.Write (2⁸)⁵ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 3³? =
  40. 40.What is the value of 5⁻¹ (as a fraction)? =

Answer key

  1. 1/9
  2. 3
  3. 1/16
  4. 7
  5. 64
  6. 1/9
  7. 0.083
  8. 72
  9. 0.00044
  10. 12
  11. 0.00098
  12. 46656
  13. 0.0003
  14. 25/4
  15. 59049
  16. 2401
  17. 5
  18. 0.00033
  19. 1/512
  20. 1/2
  21. 9
  22. 14
  23. 81
  24. 1/512
  25. 18
  26. 14
  27. 16
  28. 1
  29. 8
  30. 9/4
  31. 4096
  32. 1/10
  33. 1/100
  34. 4
  35. 0.043
  36. 9
  37. 512
  38. 40
  39. 27
  40. 1/5

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