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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 370 · 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 2⁵ × 2² as a single power 2ⁿ. What is n?
  2. 2.Write 5 × 10⁻² as a decimal. =
  3. 3.Write 9 × 10⁻³ as a decimal. =
  4. 4.Write 9,50,00,000 in standard form as 9.5 × 10ⁿ. What is n?
  5. 5.Write 3.5 × 10⁻¹ as a decimal. =
  6. 6.What is the value of 5⁴ × 5⁻⁴? =
  7. 7.Write 8.1 × 10⁻¹ as a decimal. =
  8. 8.Write 5.3 × 10⁻³ as a decimal. =
  9. 9.What is the value of 2⁵ × 2⁻¹? =
  10. 10.Write (7⁶)⁷ as a single power 7ⁿ. What is n?
  11. 11.Write 8.6 × 10⁻² as a decimal. =
  12. 12.Write 9.3 × 10⁻² as a decimal. =
  13. 13.Write 7.1 × 10⁻² as a decimal. =
  14. 14.What is the value of 2¹⁴? =
  15. 15.What is the value of 4⁵? =
  16. 16.What is the value of 4⁴? =
  17. 17.Write 3⁸ ÷ 3⁵ as a single power 3ⁿ. What is n?
  18. 18.Write 2.7 × 10⁻³ as a decimal. =
  19. 19.Write 2.4 × 10⁻¹ as a decimal. =
  20. 20.Write 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  21. 21.Write 5.1 × 10⁻¹ as a decimal. =
  22. 22.Write 9⁹ × 9⁷ as a single power 9ⁿ. What is n?
  23. 23.1.8 × 10⁵ =
  24. 24.Write 2.8 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 3⁴ × 3⁻⁴? =
  26. 26.What is the value of 4⁸? =
  27. 27.What is the value of 10³ × 10⁻²? =
  28. 28.8.7 × 10² =
  29. 29.Write (7⁴)⁸ as a single power 7ⁿ. What is n?
  30. 30.Write (5⁸)⁵ as a single power 5ⁿ. What is n?
  31. 31.What is the value of 5⁶? =
  32. 32.What is the value of 10⁵? =
  33. 33.Write 4¹⁵ ÷ 4⁷ as a single power 4ⁿ. What is n?
  34. 34.Write 8.2 × 10⁻² as a decimal. =
  35. 35.Write 8² × 8⁸ as a single power 8ⁿ. What is n?
  36. 36.Write 2⁹ × 2⁹ as a single power 2ⁿ. What is n?
  37. 37.9.6 × 10⁵ =
  38. 38.Write 9³ × 9⁹ as a single power 9ⁿ. What is n?
  39. 39.Write 71,000 in standard form as 7.1 × 10ⁿ. What is n?
  40. 40.Write 2,90,000 in standard form as 2.9 × 10ⁿ. What is n?

Answer key

  1. 7
  2. 0.05
  3. 0.009
  4. 7
  5. 0.35
  6. 1
  7. 0.81
  8. 0.0053
  9. 16
  10. 42
  11. 0.086
  12. 0.093
  13. 0.071
  14. 16384
  15. 1024
  16. 256
  17. 3
  18. 0.0027
  19. 0.24
  20. 3
  21. 0.51
  22. 16
  23. 180000
  24. 0.28
  25. 1
  26. 65536
  27. 10
  28. 870
  29. 32
  30. 40
  31. 15625
  32. 100000
  33. 8
  34. 0.082
  35. 10
  36. 18
  37. 960000
  38. 12
  39. 4
  40. 5

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