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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 802 · 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 × 5⁵ as a single power 5ⁿ. What is n?
  2. 2.Write 4¹⁷ ÷ 4⁹ as a single power 4ⁿ. What is n?
  3. 3.What is the value of 2³? =
  4. 4.Write 2.8 × 10⁻⁴ as a decimal. =
  5. 5.What is the value of (3/4)⁻²? =
  6. 6.Write 7¹³ ÷ 7⁹ as a single power 7ⁿ. What is n?
  7. 7.Write 3³ × 3⁵ as a single power 3ⁿ. What is n?
  8. 8.Write 940 in standard form as 9.4 × 10ⁿ. What is n?
  9. 9.What is the value of 10⁵ × 10⁻³? =
  10. 10.What is the value of 2¹ × 2⁻⁶? =
  11. 11.Write 8.3 × 10⁻² as a decimal. =
  12. 12.Write (6⁵)⁴ as a single power 6ⁿ. What is n?
  13. 13.What is the value of (1/4)⁻¹? =
  14. 14.Write (6⁵)² as a single power 6ⁿ. What is n?
  15. 15.Write 8⁹ ÷ 8⁴ as a single power 8ⁿ. What is n?
  16. 16.4 × 10⁶ =
  17. 17.Write 86,00,000 in standard form as 8.6 × 10ⁿ. What is n?
  18. 18.What is the value of 3⁴ × 3⁻⁵? =
  19. 19.What is the value of 2¹ × 2⁻²? =
  20. 20.What is the value of 2² × 2⁻²? =
  21. 21.Write 3.5 × 10⁻¹ as a decimal. =
  22. 22.4.6 × 10³ =
  23. 23.What is the value of 2⁸? =
  24. 24.Write 4⁴ × 4⁶ as a single power 4ⁿ. What is n?
  25. 25.Write 3⁷ × 3⁵ as a single power 3ⁿ. What is n?
  26. 26.What is the value of (2/3)⁻²? =
  27. 27.What is the value of 10³ × 10⁻⁴? =
  28. 28.Write 2,900 in standard form as 2.9 × 10ⁿ. What is n?
  29. 29.What is the value of 7⁴? =
  30. 30.What is the value of (5/6)⁻²? =
  31. 31.What is the value of 3⁹? =
  32. 32.Write 3¹⁵ ÷ 3⁹ as a single power 3ⁿ. What is n?
  33. 33.Write (5²)³ as a single power 5ⁿ. What is n?
  34. 34.What is the value of 2⁴? =
  35. 35.Write (6²)⁸ as a single power 6ⁿ. What is n?
  36. 36.Write 3.1 × 10⁻⁴ as a decimal. =
  37. 37.Write 81,000 in standard form as 8.1 × 10ⁿ. What is n?
  38. 38.6.7 × 10² =
  39. 39.Write 9.8 × 10⁻⁴ as a decimal. =
  40. 40.Write 2.2 × 10⁻⁴ as a decimal. =

Answer key

  1. 10
  2. 8
  3. 8
  4. 0.00028
  5. 16/9
  6. 4
  7. 8
  8. 2
  9. 100
  10. 1/32
  11. 0.083
  12. 20
  13. 4
  14. 10
  15. 5
  16. 4000000
  17. 6
  18. 1/3
  19. 1/2
  20. 1
  21. 0.35
  22. 4600
  23. 256
  24. 10
  25. 12
  26. 9/4
  27. 1/10
  28. 3
  29. 2401
  30. 36/25
  31. 19683
  32. 6
  33. 6
  34. 16
  35. 16
  36. 0.00031
  37. 4
  38. 670
  39. 0.00098
  40. 0.00022

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