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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 580 · 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.What is the value of 2¹³? =
  2. 2.Write 9.2 × 10⁻⁴ as a decimal. =
  3. 3.Write (7²)⁷ as a single power 7ⁿ. What is n?
  4. 4.What is the value of (2/7)⁻²? =
  5. 5.Write 4² × 4⁸ as a single power 4ⁿ. What is n?
  6. 6.What is the value of (6/7)⁻¹? =
  7. 7.What is the value of 10³? =
  8. 8.What is the value of (3/7)⁻¹? =
  9. 9.Write 3.6 × 10⁻² as a decimal. =
  10. 10.Write (2⁷)⁸ as a single power 2ⁿ. What is n?
  11. 11.What is the value of 6⁵? =
  12. 12.What is the value of 10⁵ × 10⁻²? =
  13. 13.Write (8⁹)⁹ as a single power 8ⁿ. What is n?
  14. 14.What is the value of 2⁸? =
  15. 15.Write 93,000 in standard form as 9.3 × 10ⁿ. What is n?
  16. 16.What is the value of (1/8)⁻²? =
  17. 17.What is the value of (1/8)⁻¹? =
  18. 18.Write 4¹⁷ ÷ 4⁸ as a single power 4ⁿ. What is n?
  19. 19.Write 6.8 × 10⁻² as a decimal. =
  20. 20.What is the value of 2⁶ × 2⁻⁴? =
  21. 21.What is the value of 2⁻¹ (as a fraction)? =
  22. 22.What is the value of 4⁻² (as a fraction)? =
  23. 23.Write 5.6 × 10⁻³ as a decimal. =
  24. 24.Write 75,000 in standard form as 7.5 × 10ⁿ. What is n?
  25. 25.Write 4,300 in standard form as 4.3 × 10ⁿ. What is n?
  26. 26.Write 4⁸ ÷ 4³ as a single power 4ⁿ. What is n?
  27. 27.What is the value of 3⁹? =
  28. 28.Write (7³)⁹ as a single power 7ⁿ. What is n?
  29. 29.What is the value of 5⁵? =
  30. 30.What is the value of (1/7)⁻¹? =
  31. 31.What is the value of 10¹ × 10⁻⁶? =
  32. 32.6.1 × 10⁵ =
  33. 33.What is the value of 2¹ × 2⁻⁶? =
  34. 34.Write 3⁶ × 3³ as a single power 3ⁿ. What is n?
  35. 35.What is the value of 6⁻³ (as a fraction)? =
  36. 36.Write 2 × 10⁻¹ as a decimal. =
  37. 37.What is the value of 3⁶ × 3⁻⁵? =
  38. 38.Write 9.5 × 10⁻⁴ as a decimal. =
  39. 39.Write 5.7 × 10⁻¹ as a decimal. =
  40. 40.What is the value of 2¹¹? =

Answer key

  1. 8192
  2. 0.00092
  3. 14
  4. 49/4
  5. 10
  6. 7/6
  7. 1000
  8. 7/3
  9. 0.036
  10. 56
  11. 7776
  12. 1000
  13. 81
  14. 256
  15. 4
  16. 64
  17. 8
  18. 9
  19. 0.068
  20. 4
  21. 1/2
  22. 1/16
  23. 0.0056
  24. 4
  25. 3
  26. 5
  27. 19683
  28. 27
  29. 3125
  30. 7
  31. 1/100000
  32. 610000
  33. 1/32
  34. 9
  35. 1/216
  36. 0.2
  37. 3
  38. 0.00095
  39. 0.57
  40. 2048

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