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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 540 · 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 2.3 × 10⁻³ as a decimal. =
  2. 2.What is the value of 7⁻¹ (as a fraction)? =
  3. 3.6.7 × 10³ =
  4. 4.Write (8²)⁵ as a single power 8ⁿ. What is n?
  5. 5.Write 3¹⁰ ÷ 3⁶ as a single power 3ⁿ. What is n?
  6. 6.Write 27,000 in standard form as 2.7 × 10ⁿ. What is n?
  7. 7.What is the value of (6/7)⁻²? =
  8. 8.What is the value of 4⁴? =
  9. 9.What is the value of 2¹⁵? =
  10. 10.Write (7⁴)² as a single power 7ⁿ. What is n?
  11. 11.5.6 × 10⁵ =
  12. 12.Write 660 in standard form as 6.6 × 10ⁿ. What is n?
  13. 13.Write 2.3 × 10⁻⁴ as a decimal. =
  14. 14.What is the value of (5/8)⁻²? =
  15. 15.What is the value of 5¹ × 5⁻⁶? =
  16. 16.Write 2.8 × 10⁻² as a decimal. =
  17. 17.What is the value of 8²? =
  18. 18.What is the value of (2/3)⁻¹? =
  19. 19.What is the value of 3⁴ × 3⁻⁵? =
  20. 20.Write 9⁴ × 9⁴ as a single power 9ⁿ. What is n?
  21. 21.Write (9³)⁵ as a single power 9ⁿ. What is n?
  22. 22.Write 8,900 in standard form as 8.9 × 10ⁿ. What is n?
  23. 23.What is the value of 2⁻⁸ (as a fraction)? =
  24. 24.What is the value of 9⁻² (as a fraction)? =
  25. 25.6.6 × 10⁶ =
  26. 26.What is the value of 5² × 5⁻³? =
  27. 27.Write 4¹² ÷ 4⁹ as a single power 4ⁿ. What is n?
  28. 28.Write 5.7 × 10⁻² as a decimal. =
  29. 29.Write 4.7 × 10⁻² as a decimal. =
  30. 30.Write 3⁴ × 3⁶ as a single power 3ⁿ. What is n?
  31. 31.8.3 × 10⁵ =
  32. 32.What is the value of 5⁷? =
  33. 33.What is the value of (3/5)⁻²? =
  34. 34.What is the value of 9⁴? =
  35. 35.What is the value of 2⁹? =
  36. 36.Write 4² × 4³ as a single power 4ⁿ. What is n?
  37. 37.What is the value of 3⁵ × 3⁻⁶? =
  38. 38.What is the value of 3³? =
  39. 39.What is the value of 2³ × 2⁻¹? =
  40. 40.Write 8.9 × 10⁻² as a decimal. =

Answer key

  1. 0.0023
  2. 1/7
  3. 6700
  4. 10
  5. 4
  6. 4
  7. 49/36
  8. 256
  9. 32768
  10. 8
  11. 560000
  12. 2
  13. 0.00023
  14. 64/25
  15. 1/3125
  16. 0.028
  17. 64
  18. 3/2
  19. 1/3
  20. 8
  21. 15
  22. 3
  23. 1/256
  24. 1/81
  25. 6600000
  26. 1/5
  27. 3
  28. 0.057
  29. 0.047
  30. 10
  31. 830000
  32. 78125
  33. 25/9
  34. 6561
  35. 512
  36. 5
  37. 1/3
  38. 27
  39. 4
  40. 0.089

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