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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 15 · 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 3² × 3⁸ as a single power 3ⁿ. What is n?
  2. 2.4.6 × 10⁶ =
  3. 3.What is the value of 2¹⁰? =
  4. 4.What is the value of 3⁻² (as a fraction)? =
  5. 5.What is the value of 5² × 5⁻³? =
  6. 6.What is the value of 3⁷? =
  7. 7.Write 3,80,000 in standard form as 3.8 × 10ⁿ. What is n?
  8. 8.What is the value of 8⁴? =
  9. 9.What is the value of (1/7)⁻¹? =
  10. 10.Write 5.8 × 10⁻³ as a decimal. =
  11. 11.Write (8³)³ as a single power 8ⁿ. What is n?
  12. 12.Write 6.7 × 10⁻⁴ as a decimal. =
  13. 13.2.6 × 10⁷ =
  14. 14.What is the value of 8⁵? =
  15. 15.What is the value of 5⁵ × 5⁻²? =
  16. 16.What is the value of 3¹ × 3⁻²? =
  17. 17.Write (6⁸)⁷ as a single power 6ⁿ. What is n?
  18. 18.Write 7³ × 7³ as a single power 7ⁿ. What is n?
  19. 19.1.7 × 10⁶ =
  20. 20.What is the value of 8⁻³ (as a fraction)? =
  21. 21.What is the value of 2³ × 2⁻³? =
  22. 22.Write 20,000 in standard form as 2 × 10ⁿ. What is n?
  23. 23.Write 2 × 10⁻³ as a decimal. =
  24. 24.Write 3.3 × 10⁻² as a decimal. =
  25. 25.What is the value of 3⁻³ (as a fraction)? =
  26. 26.What is the value of 10⁵ × 10⁻⁵? =
  27. 27.Write 5.3 × 10⁻² as a decimal. =
  28. 28.3.3 × 10⁷ =
  29. 29.Write 3,500 in standard form as 3.5 × 10ⁿ. What is n?
  30. 30.Write 8.3 × 10⁻² as a decimal. =
  31. 31.1.5 × 10⁶ =
  32. 32.Write 1.5 × 10⁻² as a decimal. =
  33. 33.Write 360 in standard form as 3.6 × 10ⁿ. What is n?
  34. 34.What is the value of (1/5)⁻²? =
  35. 35.Write 6¹⁴ ÷ 6⁷ as a single power 6ⁿ. What is n?
  36. 36.What is the value of 6⁶? =
  37. 37.Write 5.5 × 10⁻² as a decimal. =
  38. 38.What is the value of 2⁹? =
  39. 39.Write 3.5 × 10⁻⁴ as a decimal. =
  40. 40.Write 7¹⁰ ÷ 7⁴ as a single power 7ⁿ. What is n?

Answer key

  1. 10
  2. 4600000
  3. 1024
  4. 1/9
  5. 1/5
  6. 2187
  7. 5
  8. 4096
  9. 7
  10. 0.0058
  11. 9
  12. 0.00067
  13. 26000000
  14. 32768
  15. 125
  16. 1/3
  17. 56
  18. 6
  19. 1700000
  20. 1/512
  21. 1
  22. 4
  23. 0.002
  24. 0.033
  25. 1/27
  26. 1
  27. 0.053
  28. 33000000
  29. 3
  30. 0.083
  31. 1500000
  32. 0.015
  33. 2
  34. 25
  35. 7
  36. 46656
  37. 0.055
  38. 512
  39. 0.00035
  40. 6

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