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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 679 · 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 400 in standard form as 4 × 10ⁿ. What is n?
  2. 2.Write 9⁸ × 9⁴ as a single power 9ⁿ. What is n?
  3. 3.Write 1.8 × 10⁻² as a decimal. =
  4. 4.What is the value of 2⁴ × 2⁻¹? =
  5. 5.What is the value of 4⁻² (as a fraction)? =
  6. 6.Write 8⁹ × 8⁶ as a single power 8ⁿ. What is n?
  7. 7.What is the value of 2⁻⁴ (as a fraction)? =
  8. 8.What is the value of 4⁻⁴ (as a fraction)? =
  9. 9.What is the value of 4⁵? =
  10. 10.What is the value of (2/5)⁻¹? =
  11. 11.Write 8.4 × 10⁻⁴ as a decimal. =
  12. 12.What is the value of 5¹ × 5⁻²? =
  13. 13.Write 2¹⁴ ÷ 2⁶ as a single power 2ⁿ. What is n?
  14. 14.What is the value of 9³? =
  15. 15.What is the value of (1/5)⁻¹? =
  16. 16.6.3 × 10⁷ =
  17. 17.Write 8⁶ × 8⁶ as a single power 8ⁿ. What is n?
  18. 18.Write (5⁹)² as a single power 5ⁿ. What is n?
  19. 19.What is the value of (2/5)⁻²? =
  20. 20.Write 3.9 × 10⁻² as a decimal. =
  21. 21.What is the value of 3²? =
  22. 22.What is the value of (6/7)⁻¹? =
  23. 23.Write 170 in standard form as 1.7 × 10ⁿ. What is n?
  24. 24.What is the value of 3¹ × 3⁻²? =
  25. 25.Write 6.2 × 10⁻³ as a decimal. =
  26. 26.Write (2⁷)⁷ as a single power 2ⁿ. What is n?
  27. 27.Write 3⁵ × 3² as a single power 3ⁿ. What is n?
  28. 28.Write 3⁹ × 3⁵ as a single power 3ⁿ. What is n?
  29. 29.Write 4.4 × 10⁻⁴ as a decimal. =
  30. 30.2.9 × 10⁷ =
  31. 31.Write 8.8 × 10⁻³ as a decimal. =
  32. 32.What is the value of (5/8)⁻²? =
  33. 33.What is the value of (5/6)⁻¹? =
  34. 34.Write 1.9 × 10⁻² as a decimal. =
  35. 35.What is the value of (3/5)⁻²? =
  36. 36.What is the value of 3⁻⁴ (as a fraction)? =
  37. 37.Write 8⁴ × 8⁹ as a single power 8ⁿ. What is n?
  38. 38.Write 3⁷ × 3³ as a single power 3ⁿ. What is n?
  39. 39.3.5 × 10² =
  40. 40.Write (2⁵)⁶ as a single power 2ⁿ. What is n?

Answer key

  1. 2
  2. 12
  3. 0.018
  4. 8
  5. 1/16
  6. 15
  7. 1/16
  8. 1/256
  9. 1024
  10. 5/2
  11. 0.00084
  12. 1/5
  13. 8
  14. 729
  15. 5
  16. 63000000
  17. 12
  18. 18
  19. 25/4
  20. 0.039
  21. 9
  22. 7/6
  23. 2
  24. 1/3
  25. 0.0062
  26. 49
  27. 7
  28. 14
  29. 0.00044
  30. 29000000
  31. 0.0088
  32. 64/25
  33. 6/5
  34. 0.019
  35. 25/9
  36. 1/81
  37. 13
  38. 10
  39. 350
  40. 30

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