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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 126 · 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 9³ × 9³ as a single power 9ⁿ. What is n?
  2. 2.Write 46,00,000 in standard form as 4.6 × 10ⁿ. What is n?
  3. 3.Write 9.4 × 10⁻⁴ as a decimal. =
  4. 4.6.9 × 10⁶ =
  5. 5.What is the value of 10⁵ × 10⁻¹? =
  6. 6.Write 9.1 × 10⁻³ as a decimal. =
  7. 7.What is the value of 10³? =
  8. 8.What is the value of 3³ × 3⁻³? =
  9. 9.What is the value of 8⁻³ (as a fraction)? =
  10. 10.Write 6² × 6⁸ as a single power 6ⁿ. What is n?
  11. 11.What is the value of 3⁴? =
  12. 12.Write 1.3 × 10⁻³ as a decimal. =
  13. 13.What is the value of 3⁵ × 3⁻⁶? =
  14. 14.What is the value of 10² × 10⁻⁶? =
  15. 15.What is the value of 4⁶? =
  16. 16.Write 4,50,000 in standard form as 4.5 × 10ⁿ. What is n?
  17. 17.What is the value of 2⁵ × 2⁻²? =
  18. 18.What is the value of 3⁻² (as a fraction)? =
  19. 19.Write 76,00,000 in standard form as 7.6 × 10ⁿ. What is n?
  20. 20.What is the value of 2⁶? =
  21. 21.What is the value of 5⁷? =
  22. 22.What is the value of (3/4)⁻²? =
  23. 23.What is the value of 6⁵? =
  24. 24.Write 2,90,00,000 in standard form as 2.9 × 10ⁿ. What is n?
  25. 25.Write 55,00,000 in standard form as 5.5 × 10ⁿ. What is n?
  26. 26.What is the value of 10⁻³ (as a fraction)? =
  27. 27.Write 4⁹ × 4⁹ as a single power 4ⁿ. What is n?
  28. 28.What is the value of 2⁸? =
  29. 29.What is the value of 2¹⁵? =
  30. 30.Write (5³)³ as a single power 5ⁿ. What is n?
  31. 31.2.5 × 10⁵ =
  32. 32.What is the value of 6⁴? =
  33. 33.What is the value of 3² × 3⁻²? =
  34. 34.Write 65,000 in standard form as 6.5 × 10ⁿ. What is n?
  35. 35.Write 3¹⁴ ÷ 3⁵ as a single power 3ⁿ. What is n?
  36. 36.What is the value of 2² × 2⁻²? =
  37. 37.Write 5¹² ÷ 5⁴ as a single power 5ⁿ. What is n?
  38. 38.Write (8⁹)⁴ as a single power 8ⁿ. What is n?
  39. 39.1.3 × 10⁵ =
  40. 40.What is the value of 4⁻⁴ (as a fraction)? =

Answer key

  1. 6
  2. 6
  3. 0.00094
  4. 6900000
  5. 10000
  6. 0.0091
  7. 1000
  8. 1
  9. 1/512
  10. 10
  11. 81
  12. 0.0013
  13. 1/3
  14. 1/10000
  15. 4096
  16. 5
  17. 8
  18. 1/9
  19. 6
  20. 64
  21. 78125
  22. 16/9
  23. 7776
  24. 7
  25. 6
  26. 1/1000
  27. 18
  28. 256
  29. 32768
  30. 9
  31. 250000
  32. 1296
  33. 1
  34. 4
  35. 9
  36. 1
  37. 8
  38. 36
  39. 130000
  40. 1/256

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