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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 355 · 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 (4²)⁵ as a single power 4ⁿ. What is n?
  2. 2.8.6 × 10² =
  3. 3.8.4 × 10⁶ =
  4. 4.What is the value of 5²? =
  5. 5.Write 8⁹ ÷ 8⁵ as a single power 8ⁿ. What is n?
  6. 6.Write 9.8 × 10⁻² as a decimal. =
  7. 7.Write 350 in standard form as 3.5 × 10ⁿ. What is n?
  8. 8.What is the value of 6³? =
  9. 9.Write 6 × 10⁻⁴ as a decimal. =
  10. 10.Write 47,00,000 in standard form as 4.7 × 10ⁿ. What is n?
  11. 11.What is the value of 6²? =
  12. 12.What is the value of 4⁴? =
  13. 13.What is the value of (1/2)⁻¹? =
  14. 14.What is the value of 9³? =
  15. 15.What is the value of 8⁻³ (as a fraction)? =
  16. 16.Write 1,20,00,000 in standard form as 1.2 × 10ⁿ. What is n?
  17. 17.What is the value of 10¹ × 10⁻⁶? =
  18. 18.Write 2.1 × 10⁻³ as a decimal. =
  19. 19.Write 1,900 in standard form as 1.9 × 10ⁿ. What is n?
  20. 20.3.3 × 10⁷ =
  21. 21.What is the value of (1/8)⁻²? =
  22. 22.Write 7¹⁰ ÷ 7⁸ as a single power 7ⁿ. What is n?
  23. 23.Write 6² × 6² as a single power 6ⁿ. What is n?
  24. 24.What is the value of 2⁻⁸ (as a fraction)? =
  25. 25.5.6 × 10² =
  26. 26.What is the value of 2¹ × 2⁻⁴? =
  27. 27.Write 9,90,000 in standard form as 9.9 × 10ⁿ. What is n?
  28. 28.Write 3,10,000 in standard form as 3.1 × 10ⁿ. What is n?
  29. 29.Write (4⁹)³ as a single power 4ⁿ. What is n?
  30. 30.Write 3,60,000 in standard form as 3.6 × 10ⁿ. What is n?
  31. 31.Write 1.7 × 10⁻² as a decimal. =
  32. 32.Write 5.8 × 10⁻⁴ as a decimal. =
  33. 33.Write 2⁶ × 2³ as a single power 2ⁿ. What is n?
  34. 34.What is the value of 7⁻³ (as a fraction)? =
  35. 35.What is the value of 10⁵ × 10⁻³? =
  36. 36.3.9 × 10⁵ =
  37. 37.Write 3⁸ × 3⁵ as a single power 3ⁿ. What is n?
  38. 38.What is the value of 6⁻³ (as a fraction)? =
  39. 39.What is the value of 2¹ × 2⁻²? =
  40. 40.What is the value of 2² × 2⁻⁴? =

Answer key

  1. 10
  2. 860
  3. 8400000
  4. 25
  5. 4
  6. 0.098
  7. 2
  8. 216
  9. 0.0006
  10. 6
  11. 36
  12. 256
  13. 2
  14. 729
  15. 1/512
  16. 7
  17. 1/100000
  18. 0.0021
  19. 3
  20. 33000000
  21. 64
  22. 2
  23. 4
  24. 1/256
  25. 560
  26. 1/8
  27. 5
  28. 5
  29. 27
  30. 5
  31. 0.017
  32. 0.00058
  33. 9
  34. 1/343
  35. 100
  36. 390000
  37. 13
  38. 1/216
  39. 1/2
  40. 1/4

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