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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 112 · 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. 1.7.4 × 10² =
  2. 2.What is the value of 3⁶? =
  3. 3.What is the value of 2⁶ × 2⁻³? =
  4. 4.Write 620 in standard form as 6.2 × 10ⁿ. What is n?
  5. 5.Write (3⁵)⁸ as a single power 3ⁿ. What is n?
  6. 6.What is the value of (3/5)⁻¹? =
  7. 7.Write 9.9 × 10⁻¹ as a decimal. =
  8. 8.What is the value of (1/6)⁻¹? =
  9. 9.Write 51,000 in standard form as 5.1 × 10ⁿ. What is n?
  10. 10.What is the value of (3/7)⁻¹? =
  11. 11.What is the value of 10⁻² (as a fraction)? =
  12. 12.What is the value of (2/9)⁻¹? =
  13. 13.What is the value of 5⁻² (as a fraction)? =
  14. 14.1.8 × 10⁵ =
  15. 15.Write 4.7 × 10⁻⁴ as a decimal. =
  16. 16.Write 5.6 × 10⁻² as a decimal. =
  17. 17.What is the value of 10⁴? =
  18. 18.What is the value of 4⁻³ (as a fraction)? =
  19. 19.What is the value of 8⁻¹ (as a fraction)? =
  20. 20.Write 2.4 × 10⁻⁴ as a decimal. =
  21. 21.Write 8,10,000 in standard form as 8.1 × 10ⁿ. What is n?
  22. 22.Write 2 × 10⁻² as a decimal. =
  23. 23.What is the value of 6⁻² (as a fraction)? =
  24. 24.Write 2⁷ × 2⁸ as a single power 2ⁿ. What is n?
  25. 25.What is the value of 2⁸? =
  26. 26.Write 6.7 × 10⁻² as a decimal. =
  27. 27.Write 76,00,000 in standard form as 7.6 × 10ⁿ. What is n?
  28. 28.What is the value of 7⁻² (as a fraction)? =
  29. 29.Write 1.9 × 10⁻² as a decimal. =
  30. 30.What is the value of 4²? =
  31. 31.What is the value of 8⁵? =
  32. 32.4.4 × 10⁵ =
  33. 33.Write 4¹⁶ ÷ 4⁹ as a single power 4ⁿ. What is n?
  34. 34.What is the value of 3¹ × 3⁻¹? =
  35. 35.What is the value of 3⁻⁵ (as a fraction)? =
  36. 36.Write 9.8 × 10⁻⁴ as a decimal. =
  37. 37.Write 2⁵ ÷ 2² as a single power 2ⁿ. What is n?
  38. 38.Write 1.8 × 10⁻⁴ as a decimal. =
  39. 39.What is the value of 2⁻⁴ (as a fraction)? =
  40. 40.What is the value of 7⁴? =

Answer key

  1. 740
  2. 729
  3. 8
  4. 2
  5. 40
  6. 5/3
  7. 0.99
  8. 6
  9. 4
  10. 7/3
  11. 1/100
  12. 9/2
  13. 1/25
  14. 180000
  15. 0.00047
  16. 0.056
  17. 10000
  18. 1/64
  19. 1/8
  20. 0.00024
  21. 5
  22. 0.02
  23. 1/36
  24. 15
  25. 256
  26. 0.067
  27. 6
  28. 1/49
  29. 0.019
  30. 16
  31. 32768
  32. 440000
  33. 7
  34. 1
  35. 1/243
  36. 0.00098
  37. 3
  38. 0.00018
  39. 1/16
  40. 2401

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