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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 306 · 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. 1.2.3 × 10⁵ =
  2. 2.Write 6.4 × 10⁻⁴ as a decimal. =
  3. 3.8.9 × 10⁶ =
  4. 4.Write 31,000 in standard form as 3.1 × 10ⁿ. What is n?
  5. 5.Write 4.4 × 10⁻² as a decimal. =
  6. 6.What is the value of 3⁵ × 3⁻⁴? =
  7. 7.What is the value of 3²? =
  8. 8.What is the value of 7³? =
  9. 9.What is the value of 4²? =
  10. 10.Write 9,200 in standard form as 9.2 × 10ⁿ. What is n?
  11. 11.What is the value of 2⁴? =
  12. 12.What is the value of 2¹ × 2⁻⁴? =
  13. 13.Write (9²)⁷ as a single power 9ⁿ. What is n?
  14. 14.What is the value of 2⁶ × 2⁻¹? =
  15. 15.What is the value of 2³ × 2⁻⁶? =
  16. 16.What is the value of (7/8)⁻²? =
  17. 17.Write 6.8 × 10⁻¹ as a decimal. =
  18. 18.Write 5.6 × 10⁻² as a decimal. =
  19. 19.8.6 × 10⁶ =
  20. 20.What is the value of 10² × 10⁻²? =
  21. 21.What is the value of 4⁻² (as a fraction)? =
  22. 22.What is the value of 2¹ × 2⁻¹? =
  23. 23.8.7 × 10⁷ =
  24. 24.4.4 × 10⁷ =
  25. 25.What is the value of 2⁴ × 2⁻³? =
  26. 26.Write 4.6 × 10⁻² as a decimal. =
  27. 27.What is the value of 3⁻² (as a fraction)? =
  28. 28.What is the value of (5/9)⁻²? =
  29. 29.What is the value of 10⁶ × 10⁻⁶? =
  30. 30.Write 1.9 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 2⁵? =
  32. 32.What is the value of 6²? =
  33. 33.Write 7² × 7⁸ as a single power 7ⁿ. What is n?
  34. 34.Write 9⁵ ÷ 9³ as a single power 9ⁿ. What is n?
  35. 35.What is the value of 2³? =
  36. 36.What is the value of 3⁴? =
  37. 37.Write 6⁵ × 6³ as a single power 6ⁿ. What is n?
  38. 38.What is the value of 2⁵ × 2⁻⁶? =
  39. 39.Write 5.7 × 10⁻¹ as a decimal. =
  40. 40.Write (3⁵)⁴ as a single power 3ⁿ. What is n?

Answer key

  1. 230000
  2. 0.00064
  3. 8900000
  4. 4
  5. 0.044
  6. 3
  7. 9
  8. 343
  9. 16
  10. 3
  11. 16
  12. 1/8
  13. 14
  14. 32
  15. 1/8
  16. 64/49
  17. 0.68
  18. 0.056
  19. 8600000
  20. 1
  21. 1/16
  22. 1
  23. 87000000
  24. 44000000
  25. 2
  26. 0.046
  27. 1/9
  28. 81/25
  29. 1
  30. 0.00019
  31. 32
  32. 36
  33. 10
  34. 2
  35. 8
  36. 81
  37. 8
  38. 1/2
  39. 0.57
  40. 20

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