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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 682 · 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 2⁵ × 2⁻³? =
  2. 2.What is the value of (4/9)⁻¹? =
  3. 3.What is the value of 7⁻³ (as a fraction)? =
  4. 4.Write 7,700 in standard form as 7.7 × 10ⁿ. What is n?
  5. 5.Write 900 in standard form as 9 × 10ⁿ. What is n?
  6. 6.8.2 × 10⁵ =
  7. 7.Write 5⁶ × 5² as a single power 5ⁿ. What is n?
  8. 8.Write 6⁸ ÷ 6² as a single power 6ⁿ. What is n?
  9. 9.What is the value of 4⁻⁴ (as a fraction)? =
  10. 10.What is the value of 3⁶ × 3⁻¹? =
  11. 11.What is the value of 4⁵? =
  12. 12.What is the value of 3⁸? =
  13. 13.Write 7² × 7⁴ as a single power 7ⁿ. What is n?
  14. 14.Write 2.3 × 10⁻⁴ as a decimal. =
  15. 15.9.3 × 10³ =
  16. 16.3.1 × 10⁵ =
  17. 17.Write 9.6 × 10⁻⁴ as a decimal. =
  18. 18.What is the value of 2³? =
  19. 19.What is the value of 10²? =
  20. 20.Write 4⁸ ÷ 4⁴ as a single power 4ⁿ. What is n?
  21. 21.Write 7¹⁷ ÷ 7⁹ as a single power 7ⁿ. What is n?
  22. 22.Write 8.7 × 10⁻² as a decimal. =
  23. 23.Write (9⁷)⁴ as a single power 9ⁿ. What is n?
  24. 24.Write 8¹⁰ ÷ 8⁵ as a single power 8ⁿ. What is n?
  25. 25.Write 6⁸ × 6⁸ as a single power 6ⁿ. What is n?
  26. 26.What is the value of 6⁻¹ (as a fraction)? =
  27. 27.Write 4.4 × 10⁻² as a decimal. =
  28. 28.Write 550 in standard form as 5.5 × 10ⁿ. What is n?
  29. 29.8.7 × 10³ =
  30. 30.Write 3⁵ × 3⁹ as a single power 3ⁿ. What is n?
  31. 31.Write 130 in standard form as 1.3 × 10ⁿ. What is n?
  32. 32.What is the value of 10² × 10⁻⁴? =
  33. 33.6.4 × 10³ =
  34. 34.Write 4¹¹ ÷ 4² as a single power 4ⁿ. What is n?
  35. 35.8.7 × 10⁶ =
  36. 36.7.7 × 10² =
  37. 37.What is the value of 2⁷? =
  38. 38.What is the value of (1/6)⁻¹? =
  39. 39.7.4 × 10³ =
  40. 40.Write 8 × 10⁻¹ as a decimal. =

Answer key

  1. 4
  2. 9/4
  3. 1/343
  4. 3
  5. 2
  6. 820000
  7. 8
  8. 6
  9. 1/256
  10. 243
  11. 1024
  12. 6561
  13. 6
  14. 0.00023
  15. 9300
  16. 310000
  17. 0.00096
  18. 8
  19. 100
  20. 4
  21. 8
  22. 0.087
  23. 28
  24. 5
  25. 16
  26. 1/6
  27. 0.044
  28. 2
  29. 8700
  30. 14
  31. 2
  32. 1/100
  33. 6400
  34. 9
  35. 8700000
  36. 770
  37. 128
  38. 6
  39. 7400
  40. 0.8

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