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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 751 · 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 3⁶ × 3⁻³? =
  2. 2.Write 9 × 10⁻⁴ as a decimal. =
  3. 3.Write 9² × 9⁹ as a single power 9ⁿ. What is n?
  4. 4.What is the value of 2² × 2⁻⁶? =
  5. 5.9.1 × 10⁵ =
  6. 6.What is the value of 2⁵? =
  7. 7.Write 3.5 × 10⁻⁴ as a decimal. =
  8. 8.6.5 × 10³ =
  9. 9.What is the value of 2¹⁴? =
  10. 10.What is the value of (2/3)⁻¹? =
  11. 11.What is the value of 10⁻² (as a fraction)? =
  12. 12.Write 5.6 × 10⁻¹ as a decimal. =
  13. 13.What is the value of (5/8)⁻¹? =
  14. 14.What is the value of 3³ × 3⁻⁴? =
  15. 15.Write 2.3 × 10⁻² as a decimal. =
  16. 16.Write 7.9 × 10⁻³ as a decimal. =
  17. 17.Write (3⁶)⁴ as a single power 3ⁿ. What is n?
  18. 18.What is the value of 6³? =
  19. 19.What is the value of 2⁵ × 2⁻¹? =
  20. 20.Write 6,80,000 in standard form as 6.8 × 10ⁿ. What is n?
  21. 21.What is the value of 10⁴? =
  22. 22.What is the value of 10² × 10⁻⁶? =
  23. 23.What is the value of 2⁶ × 2⁻⁶? =
  24. 24.Write 6² × 6⁶ as a single power 6ⁿ. What is n?
  25. 25.What is the value of 2¹²? =
  26. 26.What is the value of 2⁶? =
  27. 27.Write (3⁹)⁶ as a single power 3ⁿ. What is n?
  28. 28.Write 6,200 in standard form as 6.2 × 10ⁿ. What is n?
  29. 29.Write 2⁴ × 2⁹ as a single power 2ⁿ. What is n?
  30. 30.Write 2.9 × 10⁻² as a decimal. =
  31. 31.Write 1,50,00,000 in standard form as 1.5 × 10ⁿ. What is n?
  32. 32.5.3 × 10⁵ =
  33. 33.Write (3²)⁶ as a single power 3ⁿ. What is n?
  34. 34.What is the value of 3⁸? =
  35. 35.Write 630 in standard form as 6.3 × 10ⁿ. What is n?
  36. 36.What is the value of 3⁹? =
  37. 37.What is the value of 5⁴ × 5⁻³? =
  38. 38.Write 71,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  39. 39.Write 9⁸ × 9⁸ as a single power 9ⁿ. What is n?
  40. 40.1.7 × 10³ =

Answer key

  1. 27
  2. 0.0009
  3. 11
  4. 1/16
  5. 910000
  6. 32
  7. 0.00035
  8. 6500
  9. 16384
  10. 3/2
  11. 1/100
  12. 0.56
  13. 8/5
  14. 1/3
  15. 0.023
  16. 0.0079
  17. 24
  18. 216
  19. 16
  20. 5
  21. 10000
  22. 1/10000
  23. 1
  24. 8
  25. 4096
  26. 64
  27. 54
  28. 3
  29. 13
  30. 0.029
  31. 7
  32. 530000
  33. 12
  34. 6561
  35. 2
  36. 19683
  37. 5
  38. 6
  39. 16
  40. 1700

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