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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 191 · 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 (2⁴)² as a single power 2ⁿ. What is n?
  2. 2.What is the value of 2⁻⁸ (as a fraction)? =
  3. 3.Write 3.7 × 10⁻² as a decimal. =
  4. 4.4.4 × 10⁵ =
  5. 5.What is the value of 2⁶? =
  6. 6.What is the value of 2¹⁰? =
  7. 7.What is the value of 3³ × 3⁻⁴? =
  8. 8.What is the value of 4⁶? =
  9. 9.What is the value of 3⁻³ (as a fraction)? =
  10. 10.What is the value of 5³ × 5⁻⁵? =
  11. 11.Write (4³)² as a single power 4ⁿ. What is n?
  12. 12.Write (7⁴)⁵ as a single power 7ⁿ. What is n?
  13. 13.Write 8.2 × 10⁻³ as a decimal. =
  14. 14.7.1 × 10³ =
  15. 15.What is the value of 9⁵? =
  16. 16.What is the value of 10¹ × 10⁻⁶? =
  17. 17.What is the value of 10³ × 10⁻²? =
  18. 18.Write 6² × 6³ as a single power 6ⁿ. What is n?
  19. 19.Write 3.4 × 10⁻⁴ as a decimal. =
  20. 20.Write 8,600 in standard form as 8.6 × 10ⁿ. What is n?
  21. 21.Write 9⁵ × 9³ as a single power 9ⁿ. What is n?
  22. 22.Write 4⁶ × 4² as a single power 4ⁿ. What is n?
  23. 23.Write 3,700 in standard form as 3.7 × 10ⁿ. What is n?
  24. 24.What is the value of 8⁻² (as a fraction)? =
  25. 25.What is the value of 4⁷? =
  26. 26.Write 2¹⁰ ÷ 2⁶ as a single power 2ⁿ. What is n?
  27. 27.What is the value of 2² × 2⁻⁴? =
  28. 28.What is the value of 3¹ × 3⁻⁶? =
  29. 29.Write 1.8 × 10⁻⁴ as a decimal. =
  30. 30.Write 61,000 in standard form as 6.1 × 10ⁿ. What is n?
  31. 31.What is the value of 10² × 10⁻¹? =
  32. 32.What is the value of 4⁻² (as a fraction)? =
  33. 33.What is the value of 2⁵? =
  34. 34.Write 9.5 × 10⁻⁴ as a decimal. =
  35. 35.What is the value of 10⁶ × 10⁻³? =
  36. 36.What is the value of 4³? =
  37. 37.Write 5.7 × 10⁻¹ as a decimal. =
  38. 38.Write 6¹³ ÷ 6⁶ as a single power 6ⁿ. What is n?
  39. 39.What is the value of 2⁴? =
  40. 40.What is the value of 2¹³? =

Answer key

  1. 8
  2. 1/256
  3. 0.037
  4. 440000
  5. 64
  6. 1024
  7. 1/3
  8. 4096
  9. 1/27
  10. 1/25
  11. 6
  12. 20
  13. 0.0082
  14. 7100
  15. 59049
  16. 1/100000
  17. 10
  18. 5
  19. 0.00034
  20. 3
  21. 8
  22. 8
  23. 3
  24. 1/64
  25. 16384
  26. 4
  27. 1/4
  28. 1/243
  29. 0.00018
  30. 4
  31. 10
  32. 1/16
  33. 32
  34. 0.00095
  35. 1000
  36. 64
  37. 0.57
  38. 7
  39. 16
  40. 8192

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