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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 829 · 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 9,80,000 in standard form as 9.8 × 10ⁿ. What is n?
  2. 2.What is the value of 3² × 3⁻²? =
  3. 3.What is the value of 6²? =
  4. 4.2.6 × 10⁶ =
  5. 5.Write 9³ × 9⁹ as a single power 9ⁿ. What is n?
  6. 6.Write 8,200 in standard form as 8.2 × 10ⁿ. What is n?
  7. 7.What is the value of 8⁴? =
  8. 8.Write 2.2 × 10⁻³ as a decimal. =
  9. 9.What is the value of 10⁵? =
  10. 10.Write 3⁶ ÷ 3² as a single power 3ⁿ. What is n?
  11. 11.Write 89,00,000 in standard form as 8.9 × 10ⁿ. What is n?
  12. 12.What is the value of 2¹ × 2⁻⁴? =
  13. 13.What is the value of 2⁸? =
  14. 14.What is the value of 2⁻⁹ (as a fraction)? =
  15. 15.What is the value of 2⁻⁴ (as a fraction)? =
  16. 16.What is the value of 7⁻² (as a fraction)? =
  17. 17.What is the value of 3⁵ × 3⁻⁵? =
  18. 18.What is the value of 2⁵ × 2⁻²? =
  19. 19.Write 1.4 × 10⁻³ as a decimal. =
  20. 20.What is the value of (5/7)⁻²? =
  21. 21.What is the value of 6⁻³ (as a fraction)? =
  22. 22.What is the value of 3⁹? =
  23. 23.What is the value of 3⁴? =
  24. 24.What is the value of 3¹ × 3⁻²? =
  25. 25.Write 2⁵ × 2³ as a single power 2ⁿ. What is n?
  26. 26.Write 51,00,000 in standard form as 5.1 × 10ⁿ. What is n?
  27. 27.What is the value of 3⁻² (as a fraction)? =
  28. 28.What is the value of 7⁻³ (as a fraction)? =
  29. 29.What is the value of (1/3)⁻¹? =
  30. 30.What is the value of 8⁻¹ (as a fraction)? =
  31. 31.Write 2⁸ × 2² as a single power 2ⁿ. What is n?
  32. 32.What is the value of 8⁵? =
  33. 33.Write (3⁶)⁹ as a single power 3ⁿ. What is n?
  34. 34.Write 27,000 in standard form as 2.7 × 10ⁿ. What is n?
  35. 35.Write (9³)⁸ as a single power 9ⁿ. What is n?
  36. 36.What is the value of 5⁻² (as a fraction)? =
  37. 37.Write (2²)⁸ as a single power 2ⁿ. What is n?
  38. 38.Write 5,300 in standard form as 5.3 × 10ⁿ. What is n?
  39. 39.What is the value of 10⁴ × 10⁻⁵? =
  40. 40.Write 4,200 in standard form as 4.2 × 10ⁿ. What is n?

Answer key

  1. 5
  2. 1
  3. 36
  4. 2600000
  5. 12
  6. 3
  7. 4096
  8. 0.0022
  9. 100000
  10. 4
  11. 6
  12. 1/8
  13. 256
  14. 1/512
  15. 1/16
  16. 1/49
  17. 1
  18. 8
  19. 0.0014
  20. 49/25
  21. 1/216
  22. 19683
  23. 81
  24. 1/3
  25. 8
  26. 6
  27. 1/9
  28. 1/343
  29. 3
  30. 1/8
  31. 10
  32. 32768
  33. 54
  34. 4
  35. 24
  36. 1/25
  37. 16
  38. 3
  39. 1/10
  40. 3

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