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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 413 · 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 3⁵ × 3⁻³? =
  2. 2.What is the value of 5⁶? =
  3. 3.Write 32,000 in standard form as 3.2 × 10ⁿ. What is n?
  4. 4.What is the value of (4/5)⁻¹? =
  5. 5.Write (6³)⁶ as a single power 6ⁿ. What is n?
  6. 6.What is the value of 6⁻³ (as a fraction)? =
  7. 7.What is the value of 2⁻⁶ (as a fraction)? =
  8. 8.What is the value of 2³ × 2⁻⁵? =
  9. 9.What is the value of 4⁻⁴ (as a fraction)? =
  10. 10.Write 2.6 × 10⁻¹ as a decimal. =
  11. 11.What is the value of 2¹ × 2⁻⁴? =
  12. 12.Write 2,50,00,000 in standard form as 2.5 × 10ⁿ. What is n?
  13. 13.Write 6,20,00,000 in standard form as 6.2 × 10ⁿ. What is n?
  14. 14.Write 9¹⁸ ÷ 9⁹ as a single power 9ⁿ. What is n?
  15. 15.Write 2.9 × 10⁻¹ as a decimal. =
  16. 16.Write 9.5 × 10⁻⁴ as a decimal. =
  17. 17.Write 7.3 × 10⁻² as a decimal. =
  18. 18.Write 8⁶ × 8⁸ as a single power 8ⁿ. What is n?
  19. 19.Write 3⁶ × 3³ as a single power 3ⁿ. What is n?
  20. 20.Write (3⁷)⁷ as a single power 3ⁿ. What is n?
  21. 21.Write 5.4 × 10⁻³ as a decimal. =
  22. 22.What is the value of 3¹ × 3⁻³? =
  23. 23.Write 3³ × 3³ as a single power 3ⁿ. What is n?
  24. 24.What is the value of 3⁻⁴ (as a fraction)? =
  25. 25.What is the value of 8⁻³ (as a fraction)? =
  26. 26.What is the value of 3⁵ × 3⁻²? =
  27. 27.Write 4.4 × 10⁻² as a decimal. =
  28. 28.Write 9.7 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 9²? =
  30. 30.What is the value of 2²? =
  31. 31.What is the value of 2² × 2⁻¹? =
  32. 32.Write 5² × 5⁴ as a single power 5ⁿ. What is n?
  33. 33.Write 4⁴ × 4² as a single power 4ⁿ. What is n?
  34. 34.What is the value of 6⁵? =
  35. 35.Write 2.4 × 10⁻⁴ as a decimal. =
  36. 36.What is the value of 2¹⁰? =
  37. 37.What is the value of 5⁻¹ (as a fraction)? =
  38. 38.Write 6¹⁶ ÷ 6⁹ as a single power 6ⁿ. What is n?
  39. 39.Write 4 × 10⁻³ as a decimal. =
  40. 40.Write 4.4 × 10⁻⁴ as a decimal. =

Answer key

  1. 9
  2. 15625
  3. 4
  4. 5/4
  5. 18
  6. 1/216
  7. 1/64
  8. 1/4
  9. 1/256
  10. 0.26
  11. 1/8
  12. 7
  13. 7
  14. 9
  15. 0.29
  16. 0.00095
  17. 0.073
  18. 14
  19. 9
  20. 49
  21. 0.0054
  22. 1/9
  23. 6
  24. 1/81
  25. 1/512
  26. 27
  27. 0.044
  28. 0.97
  29. 81
  30. 4
  31. 2
  32. 6
  33. 6
  34. 7776
  35. 0.00024
  36. 1024
  37. 1/5
  38. 7
  39. 0.004
  40. 0.00044

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