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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 816 · 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 5⁵ × 5⁻⁵? =
  2. 2.What is the value of 5⁴ × 5⁻²? =
  3. 3.What is the value of 4²? =
  4. 4.What is the value of 5³ × 5⁻²? =
  5. 5.Write 2¹⁴ ÷ 2⁹ as a single power 2ⁿ. What is n?
  6. 6.What is the value of 2⁹? =
  7. 7.Write 1.4 × 10⁻² as a decimal. =
  8. 8.9.3 × 10⁶ =
  9. 9.Write 3³ × 3⁹ as a single power 3ⁿ. What is n?
  10. 10.What is the value of 10² × 10⁻³? =
  11. 11.What is the value of (3/4)⁻¹? =
  12. 12.8.1 × 10³ =
  13. 13.What is the value of (4/9)⁻¹? =
  14. 14.What is the value of 5⁵? =
  15. 15.2.9 × 10⁴ =
  16. 16.What is the value of 6⁵? =
  17. 17.What is the value of 3⁵ × 3⁻³? =
  18. 18.Write 5.7 × 10⁻² as a decimal. =
  19. 19.What is the value of 5⁻⁴ (as a fraction)? =
  20. 20.What is the value of (5/6)⁻¹? =
  21. 21.What is the value of 10⁻¹ (as a fraction)? =
  22. 22.Write 8.1 × 10⁻² as a decimal. =
  23. 23.What is the value of 3¹⁰? =
  24. 24.What is the value of 7⁻² (as a fraction)? =
  25. 25.Write 21,000 in standard form as 2.1 × 10ⁿ. What is n?
  26. 26.Write 4.7 × 10⁻⁴ as a decimal. =
  27. 27.What is the value of 2⁻⁹ (as a fraction)? =
  28. 28.Write 6.1 × 10⁻² as a decimal. =
  29. 29.Write 9.2 × 10⁻¹ as a decimal. =
  30. 30.Write 2.5 × 10⁻¹ as a decimal. =
  31. 31.Write 2,50,000 in standard form as 2.5 × 10ⁿ. What is n?
  32. 32.What is the value of 5⁻² (as a fraction)? =
  33. 33.What is the value of 5⁻³ (as a fraction)? =
  34. 34.Write (5⁶)⁴ as a single power 5ⁿ. What is n?
  35. 35.What is the value of 3² × 3⁻²? =
  36. 36.What is the value of 10⁻³ (as a fraction)? =
  37. 37.Write 7,300 in standard form as 7.3 × 10ⁿ. What is n?
  38. 38.5.4 × 10⁵ =
  39. 39.What is the value of 3⁴ × 3⁻³? =
  40. 40.Write 7¹⁷ ÷ 7⁸ as a single power 7ⁿ. What is n?

Answer key

  1. 1
  2. 25
  3. 16
  4. 5
  5. 5
  6. 512
  7. 0.014
  8. 9300000
  9. 12
  10. 1/10
  11. 4/3
  12. 8100
  13. 9/4
  14. 3125
  15. 29000
  16. 7776
  17. 9
  18. 0.057
  19. 1/625
  20. 6/5
  21. 1/10
  22. 0.081
  23. 59049
  24. 1/49
  25. 4
  26. 0.00047
  27. 1/512
  28. 0.061
  29. 0.92
  30. 0.25
  31. 5
  32. 1/25
  33. 1/125
  34. 24
  35. 1
  36. 1/1000
  37. 3
  38. 540000
  39. 3
  40. 9

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