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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 875 · 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 2.6 × 10⁻² as a decimal. =
  2. 2.What is the value of 2⁴ × 2⁻⁶? =
  3. 3.Write (3⁹)⁴ as a single power 3ⁿ. What is n?
  4. 4.What is the value of 10³ × 10⁻⁴? =
  5. 5.Write 4⁶ ÷ 4³ as a single power 4ⁿ. What is n?
  6. 6.3.2 × 10³ =
  7. 7.5.2 × 10⁴ =
  8. 8.Write 4,300 in standard form as 4.3 × 10ⁿ. What is n?
  9. 9.Write (8⁵)⁹ as a single power 8ⁿ. What is n?
  10. 10.Write 2.8 × 10⁻¹ as a decimal. =
  11. 11.Write 7⁹ × 7⁶ as a single power 7ⁿ. What is n?
  12. 12.What is the value of 3⁻¹ (as a fraction)? =
  13. 13.What is the value of (7/8)⁻¹? =
  14. 14.What is the value of 2⁻⁵ (as a fraction)? =
  15. 15.Write 27,00,000 in standard form as 2.7 × 10ⁿ. What is n?
  16. 16.What is the value of 10¹ × 10⁻³? =
  17. 17.Write 2.2 × 10⁻³ as a decimal. =
  18. 18.1.6 × 10⁶ =
  19. 19.Write 2³ × 2⁴ as a single power 2ⁿ. What is n?
  20. 20.What is the value of 2⁻¹ (as a fraction)? =
  21. 21.Write 3.8 × 10⁻³ as a decimal. =
  22. 22.Write 8.4 × 10⁻³ as a decimal. =
  23. 23.What is the value of 7³? =
  24. 24.Write 330 in standard form as 3.3 × 10ⁿ. What is n?
  25. 25.What is the value of 4⁸? =
  26. 26.Write 3,300 in standard form as 3.3 × 10ⁿ. What is n?
  27. 27.Write (6⁵)⁴ as a single power 6ⁿ. What is n?
  28. 28.7.2 × 10³ =
  29. 29.Write (9⁴)⁸ as a single power 9ⁿ. What is n?
  30. 30.Write 5¹¹ ÷ 5² as a single power 5ⁿ. What is n?
  31. 31.What is the value of 3⁶? =
  32. 32.What is the value of (4/9)⁻¹? =
  33. 33.Write 9.1 × 10⁻⁴ as a decimal. =
  34. 34.Write 9.5 × 10⁻² as a decimal. =
  35. 35.Write 3³ × 3⁴ as a single power 3ⁿ. What is n?
  36. 36.8.7 × 10⁵ =
  37. 37.5.4 × 10³ =
  38. 38.What is the value of 10⁶ × 10⁻²? =
  39. 39.Write 4.1 × 10⁻⁴ as a decimal. =
  40. 40.Write 7.2 × 10⁻¹ as a decimal. =

Answer key

  1. 0.026
  2. 1/4
  3. 36
  4. 1/10
  5. 3
  6. 3200
  7. 52000
  8. 3
  9. 45
  10. 0.28
  11. 15
  12. 1/3
  13. 8/7
  14. 1/32
  15. 6
  16. 1/100
  17. 0.0022
  18. 1600000
  19. 7
  20. 1/2
  21. 0.0038
  22. 0.0084
  23. 343
  24. 2
  25. 65536
  26. 3
  27. 20
  28. 7200
  29. 32
  30. 9
  31. 729
  32. 9/4
  33. 0.00091
  34. 0.095
  35. 7
  36. 870000
  37. 5400
  38. 10000
  39. 0.00041
  40. 0.72

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