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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 709 · 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 6.2 × 10⁻⁴ as a decimal. =
  2. 2.Write 9,50,000 in standard form as 9.5 × 10ⁿ. What is n?
  3. 3.What is the value of 10²? =
  4. 4.9.6 × 10⁵ =
  5. 5.Write (6²)² as a single power 6ⁿ. What is n?
  6. 6.Write (2³)⁷ as a single power 2ⁿ. What is n?
  7. 7.What is the value of 10² × 10⁻⁵? =
  8. 8.Write 6.4 × 10⁻³ as a decimal. =
  9. 9.What is the value of (1/4)⁻²? =
  10. 10.What is the value of 2⁻⁶ (as a fraction)? =
  11. 11.What is the value of (3/4)⁻¹? =
  12. 12.What is the value of 2⁴ × 2⁻³? =
  13. 13.Write 360 in standard form as 3.6 × 10ⁿ. What is n?
  14. 14.What is the value of (1/5)⁻²? =
  15. 15.Write 6.1 × 10⁻² as a decimal. =
  16. 16.What is the value of 2² × 2⁻³? =
  17. 17.6.9 × 10⁶ =
  18. 18.Write (6⁴)² as a single power 6ⁿ. What is n?
  19. 19.Write 2,40,00,000 in standard form as 2.4 × 10ⁿ. What is n?
  20. 20.Write 3 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 2¹⁴? =
  22. 22.Write 1.2 × 10⁻⁴ as a decimal. =
  23. 23.Write 6⁵ × 6³ as a single power 6ⁿ. What is n?
  24. 24.What is the value of 2² × 2⁻⁶? =
  25. 25.What is the value of 2⁸? =
  26. 26.What is the value of 7⁻² (as a fraction)? =
  27. 27.Write 5⁷ ÷ 5³ as a single power 5ⁿ. What is n?
  28. 28.What is the value of 2⁶ × 2⁻²? =
  29. 29.Write 76,000 in standard form as 7.6 × 10ⁿ. What is n?
  30. 30.Write 1.8 × 10⁻¹ as a decimal. =
  31. 31.Write 6,90,000 in standard form as 6.9 × 10ⁿ. What is n?
  32. 32.Write 1,40,00,000 in standard form as 1.4 × 10ⁿ. What is n?
  33. 33.Write 850 in standard form as 8.5 × 10ⁿ. What is n?
  34. 34.What is the value of (5/6)⁻¹? =
  35. 35.What is the value of (5/8)⁻²? =
  36. 36.Write 4⁹ ÷ 4⁶ as a single power 4ⁿ. What is n?
  37. 37.Write 6⁶ × 6⁹ as a single power 6ⁿ. What is n?
  38. 38.Write (8²)⁷ as a single power 8ⁿ. What is n?
  39. 39.Write 3.6 × 10⁻² as a decimal. =
  40. 40.Write (6⁹)⁷ as a single power 6ⁿ. What is n?

Answer key

  1. 0.00062
  2. 5
  3. 100
  4. 960000
  5. 4
  6. 21
  7. 1/1000
  8. 0.0064
  9. 16
  10. 1/64
  11. 4/3
  12. 2
  13. 2
  14. 25
  15. 0.061
  16. 1/2
  17. 6900000
  18. 8
  19. 7
  20. 0.3
  21. 16384
  22. 0.00012
  23. 8
  24. 1/16
  25. 256
  26. 1/49
  27. 4
  28. 16
  29. 4
  30. 0.18
  31. 5
  32. 7
  33. 2
  34. 6/5
  35. 64/25
  36. 3
  37. 15
  38. 14
  39. 0.036
  40. 63

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