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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 425 · 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 2⁶ ÷ 2⁴ as a single power 2ⁿ. What is n?
  2. 2.What is the value of 7⁻² (as a fraction)? =
  3. 3.Write 2.6 × 10⁻¹ as a decimal. =
  4. 4.What is the value of 4³? =
  5. 5.What is the value of 3²? =
  6. 6.What is the value of 10² × 10⁻⁶? =
  7. 7.What is the value of 2⁻² (as a fraction)? =
  8. 8.What is the value of (6/7)⁻²? =
  9. 9.What is the value of 3³ × 3⁻³? =
  10. 10.Write 2.7 × 10⁻⁴ as a decimal. =
  11. 11.What is the value of (3/8)⁻²? =
  12. 12.Write 4³ × 4⁷ as a single power 4ⁿ. What is n?
  13. 13.Write 5.9 × 10⁻³ as a decimal. =
  14. 14.What is the value of 2⁵ × 2⁻⁵? =
  15. 15.Write 3⁹ ÷ 3³ as a single power 3ⁿ. What is n?
  16. 16.Write 2¹¹ ÷ 2³ as a single power 2ⁿ. What is n?
  17. 17.Write 47,000 in standard form as 4.7 × 10ⁿ. What is n?
  18. 18.Write 5² × 5² as a single power 5ⁿ. What is n?
  19. 19.What is the value of 2¹⁵? =
  20. 20.Write (8⁶)⁹ as a single power 8ⁿ. What is n?
  21. 21.What is the value of 9²? =
  22. 22.What is the value of 6⁻³ (as a fraction)? =
  23. 23.What is the value of 10² × 10⁻⁴? =
  24. 24.Write 3.8 × 10⁻² as a decimal. =
  25. 25.What is the value of 5⁶ × 5⁻³? =
  26. 26.What is the value of (1/4)⁻²? =
  27. 27.Write (8²)⁹ as a single power 8ⁿ. What is n?
  28. 28.What is the value of 2⁶? =
  29. 29.What is the value of (1/8)⁻¹? =
  30. 30.What is the value of (5/7)⁻¹? =
  31. 31.What is the value of (2/5)⁻²? =
  32. 32.What is the value of 2⁻⁹ (as a fraction)? =
  33. 33.What is the value of 6⁵? =
  34. 34.Write (8⁷)⁹ as a single power 8ⁿ. What is n?
  35. 35.What is the value of 3⁻⁵ (as a fraction)? =
  36. 36.Write 8.7 × 10⁻² as a decimal. =
  37. 37.7.4 × 10⁵ =
  38. 38.Write 1,70,000 in standard form as 1.7 × 10ⁿ. What is n?
  39. 39.What is the value of 2⁸? =
  40. 40.4.4 × 10⁶ =

Answer key

  1. 2
  2. 1/49
  3. 0.26
  4. 64
  5. 9
  6. 1/10000
  7. 1/4
  8. 49/36
  9. 1
  10. 0.00027
  11. 64/9
  12. 10
  13. 0.0059
  14. 1
  15. 6
  16. 8
  17. 4
  18. 4
  19. 32768
  20. 54
  21. 81
  22. 1/216
  23. 1/100
  24. 0.038
  25. 125
  26. 16
  27. 18
  28. 64
  29. 8
  30. 7/5
  31. 25/4
  32. 1/512
  33. 7776
  34. 63
  35. 1/243
  36. 0.087
  37. 740000
  38. 5
  39. 256
  40. 4400000

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