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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 589 · 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.Write 4⁷ ÷ 4⁵ as a single power 4ⁿ. What is n?
  2. 2.Write 57,00,000 in standard form as 5.7 × 10ⁿ. What is n?
  3. 3.What is the value of 3⁶ × 3⁻³? =
  4. 4.Write 71,000 in standard form as 7.1 × 10ⁿ. What is n?
  5. 5.Write 8.8 × 10⁻³ as a decimal. =
  6. 6.Write (9⁸)⁹ as a single power 9ⁿ. What is n?
  7. 7.What is the value of 4⁸? =
  8. 8.Write 4¹⁵ ÷ 4⁷ as a single power 4ⁿ. What is n?
  9. 9.What is the value of 2³? =
  10. 10.Write 8¹⁰ ÷ 8² as a single power 8ⁿ. What is n?
  11. 11.What is the value of (1/7)⁻²? =
  12. 12.Write (8³)⁹ as a single power 8ⁿ. What is n?
  13. 13.Write 360 in standard form as 3.6 × 10ⁿ. What is n?
  14. 14.Write 5.4 × 10⁻⁴ as a decimal. =
  15. 15.What is the value of 3³ × 3⁻⁴? =
  16. 16.4.8 × 10² =
  17. 17.Write 7⁹ × 7² as a single power 7ⁿ. What is n?
  18. 18.What is the value of 5⁻⁴ (as a fraction)? =
  19. 19.What is the value of 2¹⁴? =
  20. 20.What is the value of 7⁻² (as a fraction)? =
  21. 21.Write 8⁴ ÷ 8² as a single power 8ⁿ. What is n?
  22. 22.What is the value of 10⁴? =
  23. 23.What is the value of (5/7)⁻²? =
  24. 24.What is the value of (2/3)⁻²? =
  25. 25.What is the value of 2¹⁰? =
  26. 26.Write 16,000 in standard form as 1.6 × 10ⁿ. What is n?
  27. 27.Write 1.5 × 10⁻⁴ as a decimal. =
  28. 28.Write 9.6 × 10⁻⁴ as a decimal. =
  29. 29.Write 3.7 × 10⁻¹ as a decimal. =
  30. 30.Write 2.2 × 10⁻³ as a decimal. =
  31. 31.What is the value of 2⁶ × 2⁻²? =
  32. 32.What is the value of 2⁶? =
  33. 33.Write 3.6 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 9³? =
  35. 35.Write 300 in standard form as 3 × 10ⁿ. What is n?
  36. 36.What is the value of (1/2)⁻¹? =
  37. 37.What is the value of 4⁶? =
  38. 38.Write (7⁵)⁷ as a single power 7ⁿ. What is n?
  39. 39.2.3 × 10² =
  40. 40.1.6 × 10² =

Answer key

  1. 2
  2. 6
  3. 27
  4. 4
  5. 0.0088
  6. 72
  7. 65536
  8. 8
  9. 8
  10. 8
  11. 49
  12. 27
  13. 2
  14. 0.00054
  15. 1/3
  16. 480
  17. 11
  18. 1/625
  19. 16384
  20. 1/49
  21. 2
  22. 10000
  23. 49/25
  24. 9/4
  25. 1024
  26. 4
  27. 0.00015
  28. 0.00096
  29. 0.37
  30. 0.0022
  31. 16
  32. 64
  33. 0.36
  34. 729
  35. 2
  36. 2
  37. 4096
  38. 35
  39. 230
  40. 160

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