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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 658 · 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 4.7 × 10⁻² as a decimal. =
  2. 2.3.6 × 10⁵ =
  3. 3.What is the value of 2⁻⁷ (as a fraction)? =
  4. 4.6.2 × 10⁵ =
  5. 5.What is the value of 3⁻⁵ (as a fraction)? =
  6. 6.What is the value of 4⁴? =
  7. 7.Write (7²)⁶ as a single power 7ⁿ. What is n?
  8. 8.What is the value of 7⁴? =
  9. 9.Write 2² × 2⁴ as a single power 2ⁿ. What is n?
  10. 10.Write 4.8 × 10⁻² as a decimal. =
  11. 11.What is the value of (2/3)⁻¹? =
  12. 12.What is the value of 3⁹? =
  13. 13.Write 4.6 × 10⁻² as a decimal. =
  14. 14.Write 3⁵ × 3⁷ as a single power 3ⁿ. What is n?
  15. 15.1.9 × 10² =
  16. 16.What is the value of 10² × 10⁻²? =
  17. 17.What is the value of 9³? =
  18. 18.What is the value of 3⁻⁶ (as a fraction)? =
  19. 19.Write 3¹⁴ ÷ 3⁵ as a single power 3ⁿ. What is n?
  20. 20.Write (4⁶)² as a single power 4ⁿ. What is n?
  21. 21.Write (4³)⁷ as a single power 4ⁿ. What is n?
  22. 22.Write 8⁸ × 8⁸ as a single power 8ⁿ. What is n?
  23. 23.What is the value of 6⁶? =
  24. 24.Write 8.1 × 10⁻¹ as a decimal. =
  25. 25.What is the value of (2/3)⁻²? =
  26. 26.What is the value of 10⁵ × 10⁻²? =
  27. 27.Write 7⁶ ÷ 7⁴ as a single power 7ⁿ. What is n?
  28. 28.6.6 × 10⁵ =
  29. 29.Write 5,400 in standard form as 5.4 × 10ⁿ. What is n?
  30. 30.Write 7.6 × 10⁻¹ as a decimal. =
  31. 31.Write 3.3 × 10⁻³ as a decimal. =
  32. 32.What is the value of 10⁶ × 10⁻⁴? =
  33. 33.Write 280 in standard form as 2.8 × 10ⁿ. What is n?
  34. 34.9.1 × 10² =
  35. 35.What is the value of 2¹⁵? =
  36. 36.4.5 × 10³ =
  37. 37.What is the value of 2⁻² (as a fraction)? =
  38. 38.Write 2.3 × 10⁻² as a decimal. =
  39. 39.What is the value of (4/5)⁻²? =
  40. 40.What is the value of 2⁻¹ (as a fraction)? =

Answer key

  1. 0.047
  2. 360000
  3. 1/128
  4. 620000
  5. 1/243
  6. 256
  7. 12
  8. 2401
  9. 6
  10. 0.048
  11. 3/2
  12. 19683
  13. 0.046
  14. 12
  15. 190
  16. 1
  17. 729
  18. 1/729
  19. 9
  20. 12
  21. 21
  22. 16
  23. 46656
  24. 0.81
  25. 9/4
  26. 1000
  27. 2
  28. 660000
  29. 3
  30. 0.76
  31. 0.0033
  32. 100
  33. 2
  34. 910
  35. 32768
  36. 4500
  37. 1/4
  38. 0.023
  39. 25/16
  40. 1/2

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