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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 835 · 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.Write 3² × 3⁹ as a single power 3ⁿ. What is n?
  2. 2.Write 9.1 × 10⁻² as a decimal. =
  3. 3.What is the value of 9²? =
  4. 4.What is the value of 2⁻³ (as a fraction)? =
  5. 5.Write 280 in standard form as 2.8 × 10ⁿ. What is n?
  6. 6.Write 5.9 × 10⁻³ as a decimal. =
  7. 7.Write 2.6 × 10⁻³ as a decimal. =
  8. 8.What is the value of 2⁵ × 2⁻²? =
  9. 9.What is the value of 10² × 10⁻¹? =
  10. 10.Write 8.8 × 10⁻² as a decimal. =
  11. 11.Write 6¹⁴ ÷ 6⁹ as a single power 6ⁿ. What is n?
  12. 12.What is the value of 3⁵? =
  13. 13.4.9 × 10⁴ =
  14. 14.1.3 × 10⁵ =
  15. 15.What is the value of 3²? =
  16. 16.Write 1.6 × 10⁻² as a decimal. =
  17. 17.What is the value of 3⁴ × 3⁻⁶? =
  18. 18.Write (2⁴)² as a single power 2ⁿ. What is n?
  19. 19.What is the value of (1/2)⁻²? =
  20. 20.Write 8¹¹ ÷ 8⁸ as a single power 8ⁿ. What is n?
  21. 21.What is the value of 3⁻⁶ (as a fraction)? =
  22. 22.Write 3.5 × 10⁻³ as a decimal. =
  23. 23.Write 9⁶ × 9⁶ as a single power 9ⁿ. What is n?
  24. 24.What is the value of 4⁵? =
  25. 25.What is the value of 3² × 3⁻²? =
  26. 26.Write 5.7 × 10⁻⁴ as a decimal. =
  27. 27.What is the value of 2² × 2⁻²? =
  28. 28.What is the value of 6⁻³ (as a fraction)? =
  29. 29.6 × 10⁴ =
  30. 30.Write 87,000 in standard form as 8.7 × 10ⁿ. What is n?
  31. 31.What is the value of 10²? =
  32. 32.What is the value of 3⁶ × 3⁻¹? =
  33. 33.5.9 × 10⁷ =
  34. 34.What is the value of 3¹⁰? =
  35. 35.2.5 × 10³ =
  36. 36.Write (8³)⁶ as a single power 8ⁿ. What is n?
  37. 37.What is the value of 2⁻⁷ (as a fraction)? =
  38. 38.What is the value of 2² × 2⁻⁵? =
  39. 39.What is the value of 4⁸? =
  40. 40.What is the value of 10⁶ × 10⁻⁵? =

Answer key

  1. 11
  2. 0.091
  3. 81
  4. 1/8
  5. 2
  6. 0.0059
  7. 0.0026
  8. 8
  9. 10
  10. 0.088
  11. 5
  12. 243
  13. 49000
  14. 130000
  15. 9
  16. 0.016
  17. 1/9
  18. 8
  19. 4
  20. 3
  21. 1/729
  22. 0.0035
  23. 12
  24. 1024
  25. 1
  26. 0.00057
  27. 1
  28. 1/216
  29. 60000
  30. 4
  31. 100
  32. 243
  33. 59000000
  34. 59049
  35. 2500
  36. 18
  37. 1/128
  38. 1/8
  39. 65536
  40. 10

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