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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 434 · 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 (5⁵)³ as a single power 5ⁿ. What is n?
  2. 2.What is the value of 9⁻² (as a fraction)? =
  3. 3.Write 3.1 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of 4⁻¹ (as a fraction)? =
  5. 5.What is the value of (2/5)⁻¹? =
  6. 6.What is the value of 2⁴ × 2⁻³? =
  7. 7.Write 4² × 4⁸ as a single power 4ⁿ. What is n?
  8. 8.What is the value of 2³ × 2⁻⁶? =
  9. 9.What is the value of 4⁻⁴ (as a fraction)? =
  10. 10.What is the value of (3/5)⁻²? =
  11. 11.Write 2 × 10⁻³ as a decimal. =
  12. 12.What is the value of 6⁵? =
  13. 13.Write 8¹⁰ ÷ 8² as a single power 8ⁿ. What is n?
  14. 14.What is the value of 2⁴? =
  15. 15.What is the value of (8/9)⁻²? =
  16. 16.7.3 × 10² =
  17. 17.Write 4.9 × 10⁻¹ as a decimal. =
  18. 18.2.5 × 10² =
  19. 19.What is the value of 6⁴? =
  20. 20.Write 6 × 10⁻³ as a decimal. =
  21. 21.What is the value of 3² × 3⁻¹? =
  22. 22.Write 7.5 × 10⁻¹ as a decimal. =
  23. 23.7.2 × 10⁴ =
  24. 24.Write (4⁵)⁷ as a single power 4ⁿ. What is n?
  25. 25.What is the value of 5⁵? =
  26. 26.Write 1.6 × 10⁻² as a decimal. =
  27. 27.Write 5.7 × 10⁻² as a decimal. =
  28. 28.Write 5,30,00,000 in standard form as 5.3 × 10ⁿ. What is n?
  29. 29.Write 4.5 × 10⁻⁴ as a decimal. =
  30. 30.Write 6⁸ × 6⁹ as a single power 6ⁿ. What is n?
  31. 31.Write 5¹² ÷ 5³ as a single power 5ⁿ. What is n?
  32. 32.Write 4⁵ ÷ 4² as a single power 4ⁿ. What is n?
  33. 33.What is the value of 3⁵? =
  34. 34.What is the value of 10¹ × 10⁻⁵? =
  35. 35.3 × 10² =
  36. 36.What is the value of (4/9)⁻¹? =
  37. 37.What is the value of 5² × 5⁻⁵? =
  38. 38.What is the value of 8⁻² (as a fraction)? =
  39. 39.Write (8⁸)⁷ as a single power 8ⁿ. What is n?
  40. 40.What is the value of 3⁻⁵ (as a fraction)? =

Answer key

  1. 15
  2. 1/81
  3. 0.00031
  4. 1/4
  5. 5/2
  6. 2
  7. 10
  8. 1/8
  9. 1/256
  10. 25/9
  11. 0.002
  12. 7776
  13. 8
  14. 16
  15. 81/64
  16. 730
  17. 0.49
  18. 250
  19. 1296
  20. 0.006
  21. 3
  22. 0.75
  23. 72000
  24. 35
  25. 3125
  26. 0.016
  27. 0.057
  28. 7
  29. 0.00045
  30. 17
  31. 9
  32. 3
  33. 243
  34. 1/10000
  35. 300
  36. 9/4
  37. 1/125
  38. 1/64
  39. 56
  40. 1/243

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