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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 386 · 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 ÷ 3⁶ as a single power 3ⁿ. What is n?
  2. 2.Write 4.2 × 10⁻⁴ as a decimal. =
  3. 3.Write 3⁹ × 3⁶ as a single power 3ⁿ. What is n?
  4. 4.Write 4⁸ ÷ 4⁴ as a single power 4ⁿ. What is n?
  5. 5.What is the value of 7²? =
  6. 6.What is the value of 4²? =
  7. 7.What is the value of 2⁻² (as a fraction)? =
  8. 8.What is the value of 3² × 3⁻²? =
  9. 9.What is the value of 3⁴ × 3⁻⁶? =
  10. 10.Write 4,50,000 in standard form as 4.5 × 10ⁿ. What is n?
  11. 11.Write (8⁶)² as a single power 8ⁿ. What is n?
  12. 12.What is the value of 3⁵ × 3⁻³? =
  13. 13.What is the value of (6/7)⁻¹? =
  14. 14.5.1 × 10⁷ =
  15. 15.Write 2 × 10⁻¹ as a decimal. =
  16. 16.What is the value of (3/8)⁻¹? =
  17. 17.Write 8² × 8³ as a single power 8ⁿ. What is n?
  18. 18.3.8 × 10⁷ =
  19. 19.5.1 × 10⁵ =
  20. 20.Write 2¹² ÷ 2³ as a single power 2ⁿ. What is n?
  21. 21.1.2 × 10⁶ =
  22. 22.What is the value of 6⁴? =
  23. 23.Write 5¹⁵ ÷ 5⁹ as a single power 5ⁿ. What is n?
  24. 24.What is the value of 3⁵ × 3⁻²? =
  25. 25.Write 1.5 × 10⁻⁴ as a decimal. =
  26. 26.Write (4⁸)⁶ as a single power 4ⁿ. What is n?
  27. 27.Write 560 in standard form as 5.6 × 10ⁿ. What is n?
  28. 28.What is the value of 2³ × 2⁻⁵? =
  29. 29.Write (5⁶)³ as a single power 5ⁿ. What is n?
  30. 30.Write 3.7 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 3⁻⁴ (as a fraction)? =
  32. 32.Write 5⁷ × 5² as a single power 5ⁿ. What is n?
  33. 33.Write 2¹¹ ÷ 2³ as a single power 2ⁿ. What is n?
  34. 34.What is the value of 9²? =
  35. 35.Write 5.3 × 10⁻³ as a decimal. =
  36. 36.Write 23,000 in standard form as 2.3 × 10ⁿ. What is n?
  37. 37.What is the value of 6⁶? =
  38. 38.Write 5.8 × 10⁻¹ as a decimal. =
  39. 39.What is the value of 2⁴ × 2⁻¹? =
  40. 40.5.8 × 10⁷ =

Answer key

  1. 7
  2. 0.00042
  3. 15
  4. 4
  5. 49
  6. 16
  7. 1/4
  8. 1
  9. 1/9
  10. 5
  11. 12
  12. 9
  13. 7/6
  14. 51000000
  15. 0.2
  16. 8/3
  17. 5
  18. 38000000
  19. 510000
  20. 9
  21. 1200000
  22. 1296
  23. 6
  24. 27
  25. 0.00015
  26. 48
  27. 2
  28. 1/4
  29. 18
  30. 0.00037
  31. 1/81
  32. 9
  33. 8
  34. 81
  35. 0.0053
  36. 4
  37. 46656
  38. 0.58
  39. 8
  40. 58000000

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