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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 574 · 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 4⁴ × 4² as a single power 4ⁿ. What is n?
  2. 2.Write 8.7 × 10⁻⁴ as a decimal. =
  3. 3.What is the value of (1/6)⁻¹? =
  4. 4.What is the value of 4⁻³ (as a fraction)? =
  5. 5.What is the value of 2¹ × 2⁻²? =
  6. 6.What is the value of 2¹ × 2⁻⁶? =
  7. 7.What is the value of 5⁶ × 5⁻²? =
  8. 8.What is the value of 8⁴? =
  9. 9.Write (6⁸)³ as a single power 6ⁿ. What is n?
  10. 10.What is the value of 5⁴ × 5⁻¹? =
  11. 11.Write (9⁹)² as a single power 9ⁿ. What is n?
  12. 12.What is the value of 3⁵? =
  13. 13.Write 1.7 × 10⁻⁴ as a decimal. =
  14. 14.Write 6¹² ÷ 6⁴ as a single power 6ⁿ. What is n?
  15. 15.Write 8⁹ ÷ 8³ as a single power 8ⁿ. What is n?
  16. 16.1.1 × 10⁷ =
  17. 17.Write 3¹² ÷ 3⁶ as a single power 3ⁿ. What is n?
  18. 18.Write 5⁴ × 5⁴ as a single power 5ⁿ. What is n?
  19. 19.What is the value of 4⁶? =
  20. 20.Write 7.1 × 10⁻² as a decimal. =
  21. 21.What is the value of 2⁶ × 2⁻¹? =
  22. 22.Write (6⁷)⁸ as a single power 6ⁿ. What is n?
  23. 23.Write 7.2 × 10⁻² as a decimal. =
  24. 24.Write 4⁸ × 4² as a single power 4ⁿ. What is n?
  25. 25.What is the value of 4⁻² (as a fraction)? =
  26. 26.What is the value of (4/9)⁻²? =
  27. 27.What is the value of 3⁶? =
  28. 28.Write 9.5 × 10⁻² as a decimal. =
  29. 29.What is the value of 6⁻² (as a fraction)? =
  30. 30.What is the value of 8⁻¹ (as a fraction)? =
  31. 31.What is the value of 3⁻⁵ (as a fraction)? =
  32. 32.What is the value of 5⁵ × 5⁻⁶? =
  33. 33.Write 8¹⁸ ÷ 8⁹ as a single power 8ⁿ. What is n?
  34. 34.Write 8⁷ × 8⁵ as a single power 8ⁿ. What is n?
  35. 35.4.7 × 10² =
  36. 36.6.2 × 10² =
  37. 37.What is the value of 2⁵? =
  38. 38.What is the value of 9⁵? =
  39. 39.Write 6,400 in standard form as 6.4 × 10ⁿ. What is n?
  40. 40.Write 1.4 × 10⁻³ as a decimal. =

Answer key

  1. 6
  2. 0.00087
  3. 6
  4. 1/64
  5. 1/2
  6. 1/32
  7. 625
  8. 4096
  9. 24
  10. 125
  11. 18
  12. 243
  13. 0.00017
  14. 8
  15. 6
  16. 11000000
  17. 6
  18. 8
  19. 4096
  20. 0.071
  21. 32
  22. 56
  23. 0.072
  24. 10
  25. 1/16
  26. 81/16
  27. 729
  28. 0.095
  29. 1/36
  30. 1/8
  31. 1/243
  32. 1/5
  33. 9
  34. 12
  35. 470
  36. 620
  37. 32
  38. 59049
  39. 3
  40. 0.0014

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