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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 782 · 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 230 in standard form as 2.3 × 10ⁿ. What is n?
  2. 2.Write 7,10,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  3. 3.What is the value of 3⁶? =
  4. 4.Write 9¹³ ÷ 9⁸ as a single power 9ⁿ. What is n?
  5. 5.Write 7.3 × 10⁻² as a decimal. =
  6. 6.What is the value of 2⁴ × 2⁻¹? =
  7. 7.What is the value of 8³? =
  8. 8.What is the value of 7⁻³ (as a fraction)? =
  9. 9.Write 8 × 10⁻¹ as a decimal. =
  10. 10.What is the value of 5⁻² (as a fraction)? =
  11. 11.Write (6³)⁷ as a single power 6ⁿ. What is n?
  12. 12.What is the value of 6⁴? =
  13. 13.What is the value of 5³ × 5⁻⁶? =
  14. 14.Write 8,10,000 in standard form as 8.1 × 10ⁿ. What is n?
  15. 15.Write 6¹⁰ ÷ 6⁴ as a single power 6ⁿ. What is n?
  16. 16.Write 8⁸ × 8² as a single power 8ⁿ. What is n?
  17. 17.What is the value of 2⁸? =
  18. 18.Write 5² × 5⁷ as a single power 5ⁿ. What is n?
  19. 19.What is the value of 2⁶ × 2⁻⁴? =
  20. 20.What is the value of 5⁴? =
  21. 21.What is the value of 8²? =
  22. 22.Write 8 × 10⁻² as a decimal. =
  23. 23.Write 65,00,000 in standard form as 6.5 × 10ⁿ. What is n?
  24. 24.Write 8.9 × 10⁻³ as a decimal. =
  25. 25.Write 9.4 × 10⁻¹ as a decimal. =
  26. 26.Write 5.5 × 10⁻⁴ as a decimal. =
  27. 27.What is the value of 3⁻¹ (as a fraction)? =
  28. 28.What is the value of 2⁵ × 2⁻⁶? =
  29. 29.Write 4.8 × 10⁻¹ as a decimal. =
  30. 30.4.1 × 10⁴ =
  31. 31.What is the value of 3⁶ × 3⁻⁶? =
  32. 32.Write 4.6 × 10⁻² as a decimal. =
  33. 33.Write 7.5 × 10⁻² as a decimal. =
  34. 34.Write (6⁷)³ as a single power 6ⁿ. What is n?
  35. 35.What is the value of (1/7)⁻¹? =
  36. 36.What is the value of (5/6)⁻²? =
  37. 37.Write 44,000 in standard form as 4.4 × 10ⁿ. What is n?
  38. 38.What is the value of 9³? =
  39. 39.What is the value of 10⁴? =
  40. 40.Write (8²)⁴ as a single power 8ⁿ. What is n?

Answer key

  1. 2
  2. 7
  3. 729
  4. 5
  5. 0.073
  6. 8
  7. 512
  8. 1/343
  9. 0.8
  10. 1/25
  11. 21
  12. 1296
  13. 1/125
  14. 5
  15. 6
  16. 10
  17. 256
  18. 9
  19. 4
  20. 625
  21. 64
  22. 0.08
  23. 6
  24. 0.0089
  25. 0.94
  26. 0.00055
  27. 1/3
  28. 1/2
  29. 0.48
  30. 41000
  31. 1
  32. 0.046
  33. 0.075
  34. 21
  35. 7
  36. 36/25
  37. 4
  38. 729
  39. 10000
  40. 8

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