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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 185 · 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 340 in standard form as 3.4 × 10ⁿ. What is n?
  2. 2.9.2 × 10³ =
  3. 3.Write 7⁸ × 7⁸ as a single power 7ⁿ. What is n?
  4. 4.Write (8³)⁶ as a single power 8ⁿ. What is n?
  5. 5.What is the value of 3⁻² (as a fraction)? =
  6. 6.What is the value of 5¹ × 5⁻¹? =
  7. 7.Write 1.7 × 10⁻⁴ as a decimal. =
  8. 8.What is the value of 3⁶? =
  9. 9.What is the value of 2³ × 2⁻³? =
  10. 10.Write (9⁸)⁵ as a single power 9ⁿ. What is n?
  11. 11.Write 7.8 × 10⁻² as a decimal. =
  12. 12.What is the value of 5² × 5⁻¹? =
  13. 13.What is the value of 3³ × 3⁻²? =
  14. 14.What is the value of (3/8)⁻²? =
  15. 15.Write 5 × 10⁻³ as a decimal. =
  16. 16.What is the value of 6⁻³ (as a fraction)? =
  17. 17.Write 6⁴ × 6³ as a single power 6ⁿ. What is n?
  18. 18.What is the value of (1/4)⁻²? =
  19. 19.What is the value of 3⁵ × 3⁻⁵? =
  20. 20.What is the value of 3⁻⁶ (as a fraction)? =
  21. 21.Write 4¹² ÷ 4⁶ as a single power 4ⁿ. What is n?
  22. 22.Write 900 in standard form as 9 × 10ⁿ. What is n?
  23. 23.What is the value of 4⁸? =
  24. 24.Write 4¹³ ÷ 4⁵ as a single power 4ⁿ. What is n?
  25. 25.What is the value of (8/9)⁻¹? =
  26. 26.What is the value of 4³? =
  27. 27.What is the value of 2¹ × 2⁻¹? =
  28. 28.7.6 × 10³ =
  29. 29.Write 120 in standard form as 1.2 × 10ⁿ. What is n?
  30. 30.What is the value of 10¹ × 10⁻⁶? =
  31. 31.What is the value of 10⁶ × 10⁻⁶? =
  32. 32.What is the value of 2²? =
  33. 33.Write (2⁴)³ as a single power 2ⁿ. What is n?
  34. 34.What is the value of 5¹ × 5⁻⁵? =
  35. 35.Write 2¹⁶ ÷ 2⁹ as a single power 2ⁿ. What is n?
  36. 36.Write 5.2 × 10⁻³ as a decimal. =
  37. 37.What is the value of 5³ × 5⁻³? =
  38. 38.Write (8⁸)⁹ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 3⁷? =
  40. 40.What is the value of 4⁶? =

Answer key

  1. 2
  2. 9200
  3. 16
  4. 18
  5. 1/9
  6. 1
  7. 0.00017
  8. 729
  9. 1
  10. 40
  11. 0.078
  12. 5
  13. 3
  14. 64/9
  15. 0.005
  16. 1/216
  17. 7
  18. 16
  19. 1
  20. 1/729
  21. 6
  22. 2
  23. 65536
  24. 8
  25. 9/8
  26. 64
  27. 1
  28. 7600
  29. 2
  30. 1/100000
  31. 1
  32. 4
  33. 12
  34. 1/625
  35. 7
  36. 0.0052
  37. 1
  38. 72
  39. 2187
  40. 4096

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