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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 818 · 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 (8²)⁵ as a single power 8ⁿ. What is n?
  2. 2.Write 6³ × 6⁷ as a single power 6ⁿ. What is n?
  3. 3.Write 880 in standard form as 8.8 × 10ⁿ. What is n?
  4. 4.What is the value of 2⁵ × 2⁻³? =
  5. 5.Write 8.2 × 10⁻³ as a decimal. =
  6. 6.What is the value of 10² × 10⁻¹? =
  7. 7.Write 7.4 × 10⁻³ as a decimal. =
  8. 8.What is the value of 2⁵ × 2⁻⁵? =
  9. 9.Write 3 × 10⁻² as a decimal. =
  10. 10.What is the value of 10⁴? =
  11. 11.Write (2⁸)³ as a single power 2ⁿ. What is n?
  12. 12.Write 2.4 × 10⁻³ as a decimal. =
  13. 13.What is the value of 10⁵ × 10⁻⁴? =
  14. 14.Write 7 × 10⁻¹ as a decimal. =
  15. 15.Write 5 × 10⁻¹ as a decimal. =
  16. 16.Write (5⁸)⁶ as a single power 5ⁿ. What is n?
  17. 17.What is the value of 2⁶ × 2⁻¹? =
  18. 18.What is the value of 2⁶ × 2⁻⁵? =
  19. 19.What is the value of 10⁻¹ (as a fraction)? =
  20. 20.What is the value of (4/5)⁻¹? =
  21. 21.6.2 × 10⁴ =
  22. 22.Write 5¹¹ ÷ 5⁶ as a single power 5ⁿ. What is n?
  23. 23.What is the value of 7⁻³ (as a fraction)? =
  24. 24.Write 6.4 × 10⁻¹ as a decimal. =
  25. 25.Write 23,00,000 in standard form as 2.3 × 10ⁿ. What is n?
  26. 26.What is the value of 8³? =
  27. 27.1.5 × 10² =
  28. 28.Write 6⁹ ÷ 6⁷ as a single power 6ⁿ. What is n?
  29. 29.8.4 × 10⁴ =
  30. 30.What is the value of 3¹ × 3⁻⁶? =
  31. 31.2.9 × 10⁷ =
  32. 32.What is the value of (8/9)⁻¹? =
  33. 33.What is the value of (1/2)⁻¹? =
  34. 34.Write (4⁵)⁹ as a single power 4ⁿ. What is n?
  35. 35.What is the value of 8²? =
  36. 36.What is the value of 4⁸? =
  37. 37.What is the value of 10⁵? =
  38. 38.Write 9.9 × 10⁻³ as a decimal. =
  39. 39.Write 9² × 9⁵ as a single power 9ⁿ. What is n?
  40. 40.Write 6¹¹ ÷ 6⁸ as a single power 6ⁿ. What is n?

Answer key

  1. 10
  2. 10
  3. 2
  4. 4
  5. 0.0082
  6. 10
  7. 0.0074
  8. 1
  9. 0.03
  10. 10000
  11. 24
  12. 0.0024
  13. 10
  14. 0.7
  15. 0.5
  16. 48
  17. 32
  18. 2
  19. 1/10
  20. 5/4
  21. 62000
  22. 5
  23. 1/343
  24. 0.64
  25. 6
  26. 512
  27. 150
  28. 2
  29. 84000
  30. 1/243
  31. 29000000
  32. 9/8
  33. 2
  34. 45
  35. 64
  36. 65536
  37. 100000
  38. 0.0099
  39. 7
  40. 3

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