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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 683 · 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.Write 3¹³ ÷ 3⁵ as a single power 3ⁿ. What is n?
  2. 2.What is the value of (1/3)⁻¹? =
  3. 3.What is the value of (3/5)⁻¹? =
  4. 4.Write 3.2 × 10⁻¹ as a decimal. =
  5. 5.What is the value of 2⁻⁹ (as a fraction)? =
  6. 6.What is the value of 2⁵? =
  7. 7.Write 6⁸ ÷ 6⁴ as a single power 6ⁿ. What is n?
  8. 8.What is the value of 10² × 10⁻¹? =
  9. 9.What is the value of 9⁴? =
  10. 10.Write (6⁸)⁵ as a single power 6ⁿ. What is n?
  11. 11.What is the value of (1/5)⁻¹? =
  12. 12.Write (3²)⁸ as a single power 3ⁿ. What is n?
  13. 13.What is the value of 2⁻⁴ (as a fraction)? =
  14. 14.What is the value of 2¹³? =
  15. 15.Write 1.1 × 10⁻² as a decimal. =
  16. 16.What is the value of 3³? =
  17. 17.Write 6⁹ ÷ 6² as a single power 6ⁿ. What is n?
  18. 18.What is the value of 3⁶? =
  19. 19.What is the value of 4⁻³ (as a fraction)? =
  20. 20.Write 1.7 × 10⁻⁴ as a decimal. =
  21. 21.What is the value of 5⁴? =
  22. 22.What is the value of 10⁶ × 10⁻⁶? =
  23. 23.What is the value of 5²? =
  24. 24.What is the value of (2/9)⁻²? =
  25. 25.What is the value of 7²? =
  26. 26.What is the value of (4/9)⁻¹? =
  27. 27.Write 96,00,000 in standard form as 9.6 × 10ⁿ. What is n?
  28. 28.Write 2.5 × 10⁻¹ as a decimal. =
  29. 29.Write (8⁸)⁸ as a single power 8ⁿ. What is n?
  30. 30.Write 6.5 × 10⁻⁴ as a decimal. =
  31. 31.Write 2.7 × 10⁻⁴ as a decimal. =
  32. 32.What is the value of (1/2)⁻¹? =
  33. 33.What is the value of 5¹ × 5⁻³? =
  34. 34.What is the value of (4/7)⁻²? =
  35. 35.Write 210 in standard form as 2.1 × 10ⁿ. What is n?
  36. 36.Write 2⁴ × 2⁶ as a single power 2ⁿ. What is n?
  37. 37.What is the value of 7⁻³ (as a fraction)? =
  38. 38.Write (6⁸)⁶ as a single power 6ⁿ. What is n?
  39. 39.What is the value of 3¹ × 3⁻²? =
  40. 40.Write 2² × 2² as a single power 2ⁿ. What is n?

Answer key

  1. 8
  2. 3
  3. 5/3
  4. 0.32
  5. 1/512
  6. 32
  7. 4
  8. 10
  9. 6561
  10. 40
  11. 5
  12. 16
  13. 1/16
  14. 8192
  15. 0.011
  16. 27
  17. 7
  18. 729
  19. 1/64
  20. 0.00017
  21. 625
  22. 1
  23. 25
  24. 81/4
  25. 49
  26. 9/4
  27. 6
  28. 0.25
  29. 64
  30. 0.00065
  31. 0.00027
  32. 2
  33. 1/25
  34. 49/16
  35. 2
  36. 10
  37. 1/343
  38. 48
  39. 1/3
  40. 4

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