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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 190 · 40 sums
TalentJR

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 8¹¹ ÷ 8³ as a single power 8ⁿ. What is n?
  2. 2.Write 3 × 10⁻³ as a decimal. =
  3. 3.Write 4⁹ ÷ 4² as a single power 4ⁿ. What is n?
  4. 4.Write 6.3 × 10⁻⁴ as a decimal. =
  5. 5.Write 8.9 × 10⁻⁴ as a decimal. =
  6. 6.Write 1.2 × 10⁻¹ as a decimal. =
  7. 7.Write 8 × 10⁻¹ as a decimal. =
  8. 8.Write 8.5 × 10⁻² as a decimal. =
  9. 9.What is the value of 3³ × 3⁻⁴? =
  10. 10.8.3 × 10² =
  11. 11.Write (7⁹)⁸ as a single power 7ⁿ. What is n?
  12. 12.What is the value of 5³? =
  13. 13.Write 20,000 in standard form as 2 × 10ⁿ. What is n?
  14. 14.Write 3 × 10⁻⁴ as a decimal. =
  15. 15.What is the value of 3⁹? =
  16. 16.Write 3⁸ ÷ 3³ as a single power 3ⁿ. What is n?
  17. 17.Write 1.1 × 10⁻² as a decimal. =
  18. 18.What is the value of 3¹ × 3⁻¹? =
  19. 19.What is the value of 5⁴? =
  20. 20.What is the value of 2¹⁰? =
  21. 21.What is the value of 4⁸? =
  22. 22.Write 4,100 in standard form as 4.1 × 10ⁿ. What is n?
  23. 23.What is the value of 5⁻² (as a fraction)? =
  24. 24.What is the value of 10⁴ × 10⁻⁵? =
  25. 25.Write 5 × 10⁻¹ as a decimal. =
  26. 26.What is the value of 2¹ × 2⁻⁵? =
  27. 27.What is the value of 9²? =
  28. 28.What is the value of 2² × 2⁻¹? =
  29. 29.What is the value of 10⁶ × 10⁻⁵? =
  30. 30.What is the value of 10⁴? =
  31. 31.Write 5.3 × 10⁻¹ as a decimal. =
  32. 32.What is the value of 9³? =
  33. 33.Write (2⁴)⁵ as a single power 2ⁿ. What is n?
  34. 34.What is the value of 3² × 3⁻¹? =
  35. 35.Write 550 in standard form as 5.5 × 10ⁿ. What is n?
  36. 36.What is the value of (1/2)⁻¹? =
  37. 37.Write 4.8 × 10⁻¹ as a decimal. =
  38. 38.Write 6³ × 6⁹ as a single power 6ⁿ. What is n?
  39. 39.What is the value of 5² × 5⁻⁵? =
  40. 40.Write 6.9 × 10⁻¹ as a decimal. =

Answer key

  1. 8
  2. 0.003
  3. 7
  4. 0.00063
  5. 0.00089
  6. 0.12
  7. 0.8
  8. 0.085
  9. 1/3
  10. 830
  11. 72
  12. 125
  13. 4
  14. 0.0003
  15. 19683
  16. 5
  17. 0.011
  18. 1
  19. 625
  20. 1024
  21. 65536
  22. 3
  23. 1/25
  24. 1/10
  25. 0.5
  26. 1/16
  27. 81
  28. 2
  29. 10
  30. 10000
  31. 0.53
  32. 729
  33. 20
  34. 3
  35. 2
  36. 2
  37. 0.48
  38. 12
  39. 1/125
  40. 0.69

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