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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 71 · 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 6¹¹ ÷ 6² as a single power 6ⁿ. What is n?
  2. 2.What is the value of 5¹ × 5⁻⁶? =
  3. 3.Write 5.5 × 10⁻³ as a decimal. =
  4. 4.Write 8⁸ × 8⁸ as a single power 8ⁿ. What is n?
  5. 5.What is the value of (1/5)⁻¹? =
  6. 6.4.1 × 10⁴ =
  7. 7.Write 1,500 in standard form as 1.5 × 10ⁿ. What is n?
  8. 8.Write (3⁷)⁶ as a single power 3ⁿ. What is n?
  9. 9.What is the value of 2⁶ × 2⁻²? =
  10. 10.What is the value of 3⁷? =
  11. 11.What is the value of 5³? =
  12. 12.Write 7.9 × 10⁻¹ as a decimal. =
  13. 13.Write 7 × 10⁻¹ as a decimal. =
  14. 14.What is the value of 3⁶ × 3⁻³? =
  15. 15.Write 9.8 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 3⁻³ (as a fraction)? =
  17. 17.What is the value of 7²? =
  18. 18.Write 3⁷ × 3⁴ as a single power 3ⁿ. What is n?
  19. 19.Write 9.8 × 10⁻² as a decimal. =
  20. 20.Write 5¹⁴ ÷ 5⁵ as a single power 5ⁿ. What is n?
  21. 21.Write 8⁶ ÷ 8³ as a single power 8ⁿ. What is n?
  22. 22.What is the value of 3³ × 3⁻³? =
  23. 23.Write 9¹⁶ ÷ 9⁹ as a single power 9ⁿ. What is n?
  24. 24.Write 6⁴ × 6⁶ as a single power 6ⁿ. What is n?
  25. 25.What is the value of 3⁻⁶ (as a fraction)? =
  26. 26.What is the value of 3⁵? =
  27. 27.What is the value of 2¹³? =
  28. 28.What is the value of (5/8)⁻¹? =
  29. 29.Write 3,900 in standard form as 3.9 × 10ⁿ. What is n?
  30. 30.What is the value of 3² × 3⁻¹? =
  31. 31.What is the value of 4⁻⁴ (as a fraction)? =
  32. 32.What is the value of 3⁶ × 3⁻²? =
  33. 33.3.9 × 10³ =
  34. 34.What is the value of 10⁵ × 10⁻²? =
  35. 35.Write 3¹⁶ ÷ 3⁷ as a single power 3ⁿ. What is n?
  36. 36.Write 4² × 4⁶ as a single power 4ⁿ. What is n?
  37. 37.1.9 × 10⁵ =
  38. 38.8.8 × 10⁵ =
  39. 39.Write 2.4 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of 2²? =

Answer key

  1. 9
  2. 1/3125
  3. 0.0055
  4. 16
  5. 5
  6. 41000
  7. 3
  8. 42
  9. 16
  10. 2187
  11. 125
  12. 0.79
  13. 0.7
  14. 27
  15. 0.00098
  16. 1/27
  17. 49
  18. 11
  19. 0.098
  20. 9
  21. 3
  22. 1
  23. 7
  24. 10
  25. 1/729
  26. 243
  27. 8192
  28. 8/5
  29. 3
  30. 3
  31. 1/256
  32. 81
  33. 3900
  34. 1000
  35. 9
  36. 8
  37. 190000
  38. 880000
  39. 0.00024
  40. 4

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