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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 529 · 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 (5⁷)⁹ as a single power 5ⁿ. What is n?
  2. 2.What is the value of 3⁵ × 3⁻⁶? =
  3. 3.Write 2.9 × 10⁻¹ as a decimal. =
  4. 4.Write 2⁷ × 2⁵ as a single power 2ⁿ. What is n?
  5. 5.Write 6⁶ × 6² as a single power 6ⁿ. What is n?
  6. 6.What is the value of 2³? =
  7. 7.Write (3⁴)⁵ as a single power 3ⁿ. What is n?
  8. 8.Write 3¹⁶ ÷ 3⁷ as a single power 3ⁿ. What is n?
  9. 9.Write (2³)⁴ as a single power 2ⁿ. What is n?
  10. 10.What is the value of 2⁻⁶ (as a fraction)? =
  11. 11.Write 8.1 × 10⁻³ as a decimal. =
  12. 12.What is the value of 7³? =
  13. 13.4.6 × 10⁷ =
  14. 14.Write 8.9 × 10⁻³ as a decimal. =
  15. 15.Write 6.4 × 10⁻³ as a decimal. =
  16. 16.Write 2.8 × 10⁻² as a decimal. =
  17. 17.What is the value of 2¹⁵? =
  18. 18.6.4 × 10⁶ =
  19. 19.2.6 × 10⁷ =
  20. 20.What is the value of 2⁹? =
  21. 21.Write 42,00,000 in standard form as 4.2 × 10ⁿ. What is n?
  22. 22.What is the value of 5⁷? =
  23. 23.Write 4.1 × 10⁻¹ as a decimal. =
  24. 24.What is the value of 2¹¹? =
  25. 25.Write 8¹² ÷ 8³ as a single power 8ⁿ. What is n?
  26. 26.Write 7.1 × 10⁻⁴ as a decimal. =
  27. 27.Write 16,000 in standard form as 1.6 × 10ⁿ. What is n?
  28. 28.2 × 10⁵ =
  29. 29.Write 2.7 × 10⁻¹ as a decimal. =
  30. 30.Write 3.2 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 10³ × 10⁻²? =
  32. 32.What is the value of 3¹ × 3⁻³? =
  33. 33.What is the value of 3²? =
  34. 34.What is the value of 10⁴ × 10⁻⁶? =
  35. 35.Write 2.4 × 10⁻¹ as a decimal. =
  36. 36.What is the value of 2⁶ × 2⁻¹? =
  37. 37.Write 2¹⁶ ÷ 2⁷ as a single power 2ⁿ. What is n?
  38. 38.Write 9.8 × 10⁻⁴ as a decimal. =
  39. 39.What is the value of 6⁶? =
  40. 40.Write 43,00,000 in standard form as 4.3 × 10ⁿ. What is n?

Answer key

  1. 63
  2. 1/3
  3. 0.29
  4. 12
  5. 8
  6. 8
  7. 20
  8. 9
  9. 12
  10. 1/64
  11. 0.0081
  12. 343
  13. 46000000
  14. 0.0089
  15. 0.0064
  16. 0.028
  17. 32768
  18. 6400000
  19. 26000000
  20. 512
  21. 6
  22. 78125
  23. 0.41
  24. 2048
  25. 9
  26. 0.00071
  27. 4
  28. 200000
  29. 0.27
  30. 0.00032
  31. 10
  32. 1/9
  33. 9
  34. 1/100
  35. 0.24
  36. 32
  37. 9
  38. 0.00098
  39. 46656
  40. 6

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