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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 458 · 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 7⁵ × 7³ as a single power 7ⁿ. What is n?
  2. 2.Write 2¹² ÷ 2⁸ as a single power 2ⁿ. What is n?
  3. 3.Write 2² × 2⁵ as a single power 2ⁿ. What is n?
  4. 4.What is the value of 3⁶? =
  5. 5.Write 8⁶ ÷ 8² as a single power 8ⁿ. What is n?
  6. 6.Write 4.2 × 10⁻² as a decimal. =
  7. 7.Write 3² × 3⁸ as a single power 3ⁿ. What is n?
  8. 8.What is the value of 3⁴? =
  9. 9.What is the value of 5⁵ × 5⁻²? =
  10. 10.What is the value of 10⁶ × 10⁻²? =
  11. 11.Write 8.1 × 10⁻¹ as a decimal. =
  12. 12.What is the value of 2⁵ × 2⁻¹? =
  13. 13.Write (3⁸)⁹ as a single power 3ⁿ. What is n?
  14. 14.3 × 10³ =
  15. 15.What is the value of 2¹²? =
  16. 16.What is the value of 2⁶ × 2⁻⁶? =
  17. 17.Write 2 × 10⁻¹ as a decimal. =
  18. 18.What is the value of 4²? =
  19. 19.Write 92,00,000 in standard form as 9.2 × 10ⁿ. What is n?
  20. 20.What is the value of 4⁵? =
  21. 21.6.1 × 10⁶ =
  22. 22.Write 730 in standard form as 7.3 × 10ⁿ. What is n?
  23. 23.5.4 × 10² =
  24. 24.What is the value of 3²? =
  25. 25.Write 5.5 × 10⁻³ as a decimal. =
  26. 26.Write 4.3 × 10⁻² as a decimal. =
  27. 27.What is the value of (3/5)⁻²? =
  28. 28.Write 440 in standard form as 4.4 × 10ⁿ. What is n?
  29. 29.Write 28,00,000 in standard form as 2.8 × 10ⁿ. What is n?
  30. 30.Write 8.7 × 10⁻⁴ as a decimal. =
  31. 31.Write 5.2 × 10⁻³ as a decimal. =
  32. 32.What is the value of 2³ × 2⁻⁶? =
  33. 33.What is the value of 8⁵? =
  34. 34.Write 5³ × 5⁶ as a single power 5ⁿ. What is n?
  35. 35.Write (9³)⁹ as a single power 9ⁿ. What is n?
  36. 36.Write 9 × 10⁻¹ as a decimal. =
  37. 37.What is the value of 2⁻⁶ (as a fraction)? =
  38. 38.Write 8⁴ × 8⁷ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 5³ × 5⁻²? =
  40. 40.Write (3⁹)⁴ as a single power 3ⁿ. What is n?

Answer key

  1. 8
  2. 4
  3. 7
  4. 729
  5. 4
  6. 0.042
  7. 10
  8. 81
  9. 125
  10. 10000
  11. 0.81
  12. 16
  13. 72
  14. 3000
  15. 4096
  16. 1
  17. 0.2
  18. 16
  19. 6
  20. 1024
  21. 6100000
  22. 2
  23. 540
  24. 9
  25. 0.0055
  26. 0.043
  27. 25/9
  28. 2
  29. 6
  30. 0.00087
  31. 0.0052
  32. 1/8
  33. 32768
  34. 9
  35. 27
  36. 0.9
  37. 1/64
  38. 11
  39. 5
  40. 36

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