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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 943 · 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.What is the value of 3⁻² (as a fraction)? =
  2. 2.What is the value of 10¹ × 10⁻⁵? =
  3. 3.Write 3.6 × 10⁻¹ as a decimal. =
  4. 4.Write 3,60,00,000 in standard form as 3.6 × 10ⁿ. What is n?
  5. 5.What is the value of (1/3)⁻¹? =
  6. 6.What is the value of 2³? =
  7. 7.What is the value of 10⁻² (as a fraction)? =
  8. 8.What is the value of 2¹²? =
  9. 9.Write 32,000 in standard form as 3.2 × 10ⁿ. What is n?
  10. 10.Write 2¹¹ ÷ 2⁷ as a single power 2ⁿ. What is n?
  11. 11.Write 87,000 in standard form as 8.7 × 10ⁿ. What is n?
  12. 12.Write 1,90,00,000 in standard form as 1.9 × 10ⁿ. What is n?
  13. 13.What is the value of 2⁻⁶ (as a fraction)? =
  14. 14.Write 8.6 × 10⁻¹ as a decimal. =
  15. 15.Write 1.5 × 10⁻¹ as a decimal. =
  16. 16.What is the value of 10⁵ × 10⁻⁵? =
  17. 17.Write 9.2 × 10⁻² as a decimal. =
  18. 18.Write 39,000 in standard form as 3.9 × 10ⁿ. What is n?
  19. 19.What is the value of 3⁸? =
  20. 20.What is the value of 2¹ × 2⁻⁴? =
  21. 21.What is the value of 6⁻³ (as a fraction)? =
  22. 22.What is the value of 6⁴? =
  23. 23.5.7 × 10⁷ =
  24. 24.5.4 × 10⁶ =
  25. 25.1.4 × 10⁵ =
  26. 26.Write (6⁴)³ as a single power 6ⁿ. What is n?
  27. 27.What is the value of 3³? =
  28. 28.What is the value of 2⁻⁵ (as a fraction)? =
  29. 29.4 × 10² =
  30. 30.Write 6⁶ × 6⁶ as a single power 6ⁿ. What is n?
  31. 31.Write 3.5 × 10⁻⁴ as a decimal. =
  32. 32.Write 3¹¹ ÷ 3⁴ as a single power 3ⁿ. What is n?
  33. 33.Write 1.8 × 10⁻² as a decimal. =
  34. 34.Write 51,000 in standard form as 5.1 × 10ⁿ. What is n?
  35. 35.2.7 × 10⁴ =
  36. 36.What is the value of (2/3)⁻²? =
  37. 37.What is the value of (1/9)⁻²? =
  38. 38.What is the value of 4²? =
  39. 39.Write 8⁸ × 8⁴ as a single power 8ⁿ. What is n?
  40. 40.Write 9¹² ÷ 9⁷ as a single power 9ⁿ. What is n?

Answer key

  1. 1/9
  2. 1/10000
  3. 0.36
  4. 7
  5. 3
  6. 8
  7. 1/100
  8. 4096
  9. 4
  10. 4
  11. 4
  12. 7
  13. 1/64
  14. 0.86
  15. 0.15
  16. 1
  17. 0.092
  18. 4
  19. 6561
  20. 1/8
  21. 1/216
  22. 1296
  23. 57000000
  24. 5400000
  25. 140000
  26. 12
  27. 27
  28. 1/32
  29. 400
  30. 12
  31. 0.00035
  32. 7
  33. 0.018
  34. 4
  35. 27000
  36. 9/4
  37. 81
  38. 16
  39. 12
  40. 5

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