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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 344 · 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 5⁻¹ (as a fraction)? =
  2. 2.Write 3¹⁰ ÷ 3⁵ as a single power 3ⁿ. What is n?
  3. 3.What is the value of 5² × 5⁻¹? =
  4. 4.6.8 × 10⁵ =
  5. 5.What is the value of (1/7)⁻¹? =
  6. 6.What is the value of 10⁵? =
  7. 7.What is the value of 2⁷? =
  8. 8.What is the value of (1/8)⁻¹? =
  9. 9.Write 9.1 × 10⁻¹ as a decimal. =
  10. 10.What is the value of 9³? =
  11. 11.Write 3⁷ × 3⁴ as a single power 3ⁿ. What is n?
  12. 12.Write 9³ × 9² as a single power 9ⁿ. What is n?
  13. 13.What is the value of 2¹³? =
  14. 14.Write 9.3 × 10⁻² as a decimal. =
  15. 15.What is the value of 2⁵ × 2⁻⁵? =
  16. 16.Write 2.9 × 10⁻³ as a decimal. =
  17. 17.What is the value of 3⁵ × 3⁻³? =
  18. 18.Write (7⁸)⁹ as a single power 7ⁿ. What is n?
  19. 19.Write (9²)⁴ as a single power 9ⁿ. What is n?
  20. 20.What is the value of 3⁴ × 3⁻⁴? =
  21. 21.What is the value of 10¹ × 10⁻⁴? =
  22. 22.What is the value of (2/3)⁻¹? =
  23. 23.What is the value of 2¹¹? =
  24. 24.Write (6⁶)⁶ as a single power 6ⁿ. What is n?
  25. 25.What is the value of 7⁵? =
  26. 26.What is the value of 3¹ × 3⁻²? =
  27. 27.What is the value of 2² × 2⁻¹? =
  28. 28.What is the value of 4⁶? =
  29. 29.Write 9.9 × 10⁻⁴ as a decimal. =
  30. 30.Write 2⁸ ÷ 2² as a single power 2ⁿ. What is n?
  31. 31.Write 8¹⁷ ÷ 8⁹ as a single power 8ⁿ. What is n?
  32. 32.What is the value of (1/8)⁻²? =
  33. 33.What is the value of 3⁻³ (as a fraction)? =
  34. 34.What is the value of 6²? =
  35. 35.8.9 × 10³ =
  36. 36.Write 4¹⁷ ÷ 4⁹ as a single power 4ⁿ. What is n?
  37. 37.2.2 × 10² =
  38. 38.3.9 × 10⁷ =
  39. 39.What is the value of 5⁴ × 5⁻⁶? =
  40. 40.Write 5.7 × 10⁻⁴ as a decimal. =

Answer key

  1. 1/5
  2. 5
  3. 5
  4. 680000
  5. 7
  6. 100000
  7. 128
  8. 8
  9. 0.91
  10. 729
  11. 11
  12. 5
  13. 8192
  14. 0.093
  15. 1
  16. 0.0029
  17. 9
  18. 72
  19. 8
  20. 1
  21. 1/1000
  22. 3/2
  23. 2048
  24. 36
  25. 16807
  26. 1/3
  27. 2
  28. 4096
  29. 0.00099
  30. 6
  31. 8
  32. 64
  33. 1/27
  34. 36
  35. 8900
  36. 8
  37. 220
  38. 39000000
  39. 1/25
  40. 0.00057

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