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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 889 · 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 4⁹ ÷ 4⁴ as a single power 4ⁿ. What is n?
  2. 2.What is the value of 2¹ × 2⁻²? =
  3. 3.What is the value of 3⁻⁵ (as a fraction)? =
  4. 4.What is the value of 2⁻⁷ (as a fraction)? =
  5. 5.Write 58,000 in standard form as 5.8 × 10ⁿ. What is n?
  6. 6.What is the value of 4⁻² (as a fraction)? =
  7. 7.Write 180 in standard form as 1.8 × 10ⁿ. What is n?
  8. 8.Write (2⁵)⁸ as a single power 2ⁿ. What is n?
  9. 9.Write 5⁴ × 5⁷ as a single power 5ⁿ. What is n?
  10. 10.What is the value of 3³ × 3⁻³? =
  11. 11.What is the value of 5³ × 5⁻¹? =
  12. 12.What is the value of 2⁻³ (as a fraction)? =
  13. 13.What is the value of 5⁶ × 5⁻²? =
  14. 14.What is the value of (3/7)⁻¹? =
  15. 15.What is the value of 10⁻³ (as a fraction)? =
  16. 16.What is the value of 2⁵ × 2⁻¹? =
  17. 17.Write (5⁶)⁶ as a single power 5ⁿ. What is n?
  18. 18.What is the value of 2⁶ × 2⁻¹? =
  19. 19.What is the value of 5⁴? =
  20. 20.Write 3,000 in standard form as 3 × 10ⁿ. What is n?
  21. 21.What is the value of 3² × 3⁻⁴? =
  22. 22.What is the value of 3⁵ × 3⁻⁶? =
  23. 23.Write 3⁸ × 3⁵ as a single power 3ⁿ. What is n?
  24. 24.Write 3⁹ ÷ 3⁴ as a single power 3ⁿ. What is n?
  25. 25.Write 2³ × 2⁸ as a single power 2ⁿ. What is n?
  26. 26.5.2 × 10⁷ =
  27. 27.Write 9² × 9⁶ as a single power 9ⁿ. What is n?
  28. 28.Write 8⁹ × 8⁶ as a single power 8ⁿ. What is n?
  29. 29.Write (2³)⁶ as a single power 2ⁿ. What is n?
  30. 30.Write (4⁸)⁹ as a single power 4ⁿ. What is n?
  31. 31.8.6 × 10² =
  32. 32.What is the value of 10⁻¹ (as a fraction)? =
  33. 33.Write 1.9 × 10⁻⁴ as a decimal. =
  34. 34.What is the value of 9⁴? =
  35. 35.Write 7¹⁰ ÷ 7⁶ as a single power 7ⁿ. What is n?
  36. 36.Write 8³ × 8⁷ as a single power 8ⁿ. What is n?
  37. 37.What is the value of (1/7)⁻¹? =
  38. 38.What is the value of (1/8)⁻¹? =
  39. 39.What is the value of 3¹ × 3⁻³? =
  40. 40.What is the value of (1/4)⁻²? =

Answer key

  1. 5
  2. 1/2
  3. 1/243
  4. 1/128
  5. 4
  6. 1/16
  7. 2
  8. 40
  9. 11
  10. 1
  11. 25
  12. 1/8
  13. 625
  14. 7/3
  15. 1/1000
  16. 16
  17. 36
  18. 32
  19. 625
  20. 3
  21. 1/9
  22. 1/3
  23. 13
  24. 5
  25. 11
  26. 52000000
  27. 8
  28. 15
  29. 18
  30. 72
  31. 860
  32. 1/10
  33. 0.00019
  34. 6561
  35. 4
  36. 10
  37. 7
  38. 8
  39. 1/9
  40. 16

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