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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 274 · 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.What is the value of (6/7)⁻²? =
  2. 2.What is the value of 2² × 2⁻³? =
  3. 3.What is the value of (3/4)⁻¹? =
  4. 4.What is the value of 2⁴ × 2⁻⁴? =
  5. 5.Write (2⁷)² as a single power 2ⁿ. What is n?
  6. 6.Write 86,000 in standard form as 8.6 × 10ⁿ. What is n?
  7. 7.1.7 × 10⁴ =
  8. 8.Write (8⁴)² as a single power 8ⁿ. What is n?
  9. 9.Write 5³ × 5⁹ as a single power 5ⁿ. What is n?
  10. 10.Write 6⁸ × 6² as a single power 6ⁿ. What is n?
  11. 11.Write 9⁹ ÷ 9² as a single power 9ⁿ. What is n?
  12. 12.What is the value of 3⁵ × 3⁻³? =
  13. 13.What is the value of 10⁵ × 10⁻⁴? =
  14. 14.What is the value of 3⁴ × 3⁻⁵? =
  15. 15.Write 2³ × 2² as a single power 2ⁿ. What is n?
  16. 16.Write 7⁶ × 7⁸ as a single power 7ⁿ. What is n?
  17. 17.Write 3 × 10⁻⁴ as a decimal. =
  18. 18.What is the value of 4⁴? =
  19. 19.Write (9⁴)⁵ as a single power 9ⁿ. What is n?
  20. 20.Write 6⁵ × 6⁹ as a single power 6ⁿ. What is n?
  21. 21.What is the value of 10³ × 10⁻¹? =
  22. 22.What is the value of 2⁵ × 2⁻¹? =
  23. 23.Write 5,20,000 in standard form as 5.2 × 10ⁿ. What is n?
  24. 24.What is the value of 5³ × 5⁻¹? =
  25. 25.Write 4,10,000 in standard form as 4.1 × 10ⁿ. What is n?
  26. 26.5.6 × 10⁴ =
  27. 27.What is the value of 7⁻² (as a fraction)? =
  28. 28.Write 9.9 × 10⁻³ as a decimal. =
  29. 29.What is the value of 2⁵? =
  30. 30.8.6 × 10² =
  31. 31.What is the value of 2³? =
  32. 32.What is the value of 2¹¹? =
  33. 33.Write 9,50,000 in standard form as 9.5 × 10ⁿ. What is n?
  34. 34.What is the value of 2⁻⁴ (as a fraction)? =
  35. 35.What is the value of 2¹ × 2⁻²? =
  36. 36.9.1 × 10² =
  37. 37.What is the value of 9⁴? =
  38. 38.What is the value of 2⁵ × 2⁻³? =
  39. 39.What is the value of 2⁷? =
  40. 40.What is the value of 2³ × 2⁻⁶? =

Answer key

  1. 49/36
  2. 1/2
  3. 4/3
  4. 1
  5. 14
  6. 4
  7. 17000
  8. 8
  9. 12
  10. 10
  11. 7
  12. 9
  13. 10
  14. 1/3
  15. 5
  16. 14
  17. 0.0003
  18. 256
  19. 20
  20. 14
  21. 100
  22. 16
  23. 5
  24. 25
  25. 5
  26. 56000
  27. 1/49
  28. 0.0099
  29. 32
  30. 860
  31. 8
  32. 2048
  33. 5
  34. 1/16
  35. 1/2
  36. 910
  37. 6561
  38. 4
  39. 128
  40. 1/8

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