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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 638 · 40 sums
TalentJR

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 2⁻⁴ (as a fraction)? =
  2. 2.8.3 × 10⁴ =
  3. 3.What is the value of 6⁻² (as a fraction)? =
  4. 4.What is the value of 7⁻¹ (as a fraction)? =
  5. 5.What is the value of 9²? =
  6. 6.What is the value of 6⁵? =
  7. 7.Write 1,400 in standard form as 1.4 × 10ⁿ. What is n?
  8. 8.What is the value of (1/9)⁻¹? =
  9. 9.Write 3⁸ × 3⁹ as a single power 3ⁿ. What is n?
  10. 10.Write 2³ × 2⁷ as a single power 2ⁿ. What is n?
  11. 11.What is the value of 3² × 3⁻⁶? =
  12. 12.What is the value of 3⁻¹ (as a fraction)? =
  13. 13.Write 8⁹ × 8⁴ as a single power 8ⁿ. What is n?
  14. 14.What is the value of 2⁶? =
  15. 15.4.7 × 10⁶ =
  16. 16.6.6 × 10⁵ =
  17. 17.Write 11,00,000 in standard form as 1.1 × 10ⁿ. What is n?
  18. 18.What is the value of 2⁻⁸ (as a fraction)? =
  19. 19.What is the value of 10⁴ × 10⁻⁶? =
  20. 20.Write 4.2 × 10⁻⁴ as a decimal. =
  21. 21.2.3 × 10⁴ =
  22. 22.What is the value of 10⁶ × 10⁻⁵? =
  23. 23.What is the value of 2² × 2⁻⁵? =
  24. 24.What is the value of 4⁵? =
  25. 25.What is the value of 3⁴ × 3⁻²? =
  26. 26.Write 1.4 × 10⁻² as a decimal. =
  27. 27.Write 5,70,00,000 in standard form as 5.7 × 10ⁿ. What is n?
  28. 28.Write 9.8 × 10⁻¹ as a decimal. =
  29. 29.Write 480 in standard form as 4.8 × 10ⁿ. What is n?
  30. 30.7 × 10² =
  31. 31.Write 8.4 × 10⁻¹ as a decimal. =
  32. 32.Write 3⁸ × 3³ as a single power 3ⁿ. What is n?
  33. 33.Write 2² × 2² as a single power 2ⁿ. What is n?
  34. 34.Write 8.6 × 10⁻³ as a decimal. =
  35. 35.What is the value of 10⁵ × 10⁻⁵? =
  36. 36.1.5 × 10⁷ =
  37. 37.What is the value of 3⁹? =
  38. 38.What is the value of 9⁻¹ (as a fraction)? =
  39. 39.Write 3⁵ × 3² as a single power 3ⁿ. What is n?
  40. 40.Write (2⁴)⁴ as a single power 2ⁿ. What is n?

Answer key

  1. 1/16
  2. 83000
  3. 1/36
  4. 1/7
  5. 81
  6. 7776
  7. 3
  8. 9
  9. 17
  10. 10
  11. 1/81
  12. 1/3
  13. 13
  14. 64
  15. 4700000
  16. 660000
  17. 6
  18. 1/256
  19. 1/100
  20. 0.00042
  21. 23000
  22. 10
  23. 1/8
  24. 1024
  25. 9
  26. 0.014
  27. 7
  28. 0.98
  29. 2
  30. 700
  31. 0.84
  32. 11
  33. 4
  34. 0.0086
  35. 1
  36. 15000000
  37. 19683
  38. 1/9
  39. 7
  40. 16

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