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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 172 · 40 sums
TalentJR

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 2⁻⁷ (as a fraction)? =
  2. 2.Write 79,000 in standard form as 7.9 × 10ⁿ. What is n?
  3. 3.Write 9.2 × 10⁻³ as a decimal. =
  4. 4.What is the value of 3⁻¹ (as a fraction)? =
  5. 5.What is the value of 10²? =
  6. 6.What is the value of 10⁴ × 10⁻⁶? =
  7. 7.What is the value of 2⁸? =
  8. 8.What is the value of (3/4)⁻²? =
  9. 9.What is the value of 2⁵ × 2⁻¹? =
  10. 10.Write (3²)⁴ as a single power 3ⁿ. What is n?
  11. 11.What is the value of 4⁸? =
  12. 12.What is the value of 8⁻³ (as a fraction)? =
  13. 13.What is the value of 2⁹? =
  14. 14.Write 8 × 10⁻¹ as a decimal. =
  15. 15.Write 3.9 × 10⁻⁴ as a decimal. =
  16. 16.Write (4⁹)⁴ as a single power 4ⁿ. What is n?
  17. 17.Write 8.3 × 10⁻⁴ as a decimal. =
  18. 18.Write 5.1 × 10⁻² as a decimal. =
  19. 19.What is the value of 6⁻² (as a fraction)? =
  20. 20.Write 9.2 × 10⁻⁴ as a decimal. =
  21. 21.Write 2.5 × 10⁻² as a decimal. =
  22. 22.Write (8²)³ as a single power 8ⁿ. What is n?
  23. 23.8 × 10⁶ =
  24. 24.What is the value of 3³? =
  25. 25.Write 8.5 × 10⁻¹ as a decimal. =
  26. 26.What is the value of 5⁻³ (as a fraction)? =
  27. 27.Write 9,80,000 in standard form as 9.8 × 10ⁿ. What is n?
  28. 28.7.8 × 10⁷ =
  29. 29.Write (2⁷)⁸ as a single power 2ⁿ. What is n?
  30. 30.3.4 × 10⁶ =
  31. 31.What is the value of (6/7)⁻¹? =
  32. 32.What is the value of (1/9)⁻¹? =
  33. 33.What is the value of 2¹⁰? =
  34. 34.Write 5⁹ ÷ 5⁵ as a single power 5ⁿ. What is n?
  35. 35.Write 9⁶ × 9³ as a single power 9ⁿ. What is n?
  36. 36.What is the value of 3¹ × 3⁻²? =
  37. 37.What is the value of 8²? =
  38. 38.1.4 × 10⁷ =
  39. 39.Write 9.6 × 10⁻³ as a decimal. =
  40. 40.Write 7.8 × 10⁻⁴ as a decimal. =

Answer key

  1. 1/128
  2. 4
  3. 0.0092
  4. 1/3
  5. 100
  6. 1/100
  7. 256
  8. 16/9
  9. 16
  10. 8
  11. 65536
  12. 1/512
  13. 512
  14. 0.8
  15. 0.00039
  16. 36
  17. 0.00083
  18. 0.051
  19. 1/36
  20. 0.00092
  21. 0.025
  22. 6
  23. 8000000
  24. 27
  25. 0.85
  26. 1/125
  27. 5
  28. 78000000
  29. 56
  30. 3400000
  31. 7/6
  32. 9
  33. 1024
  34. 4
  35. 9
  36. 1/3
  37. 64
  38. 14000000
  39. 0.0096
  40. 0.00078

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