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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 705 · 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 7.8 × 10⁻² as a decimal. =
  2. 2.Write 4.7 × 10⁻² as a decimal. =
  3. 3.Write 6.3 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of 5⁴ × 5⁻⁵? =
  5. 5.What is the value of 8⁻¹ (as a fraction)? =
  6. 6.9.6 × 10⁶ =
  7. 7.What is the value of 10⁴? =
  8. 8.What is the value of (7/8)⁻¹? =
  9. 9.9.3 × 10⁵ =
  10. 10.What is the value of 10³ × 10⁻¹? =
  11. 11.What is the value of 3⁷? =
  12. 12.Write 5.3 × 10⁻³ as a decimal. =
  13. 13.What is the value of 4⁶? =
  14. 14.Write 2.1 × 10⁻¹ as a decimal. =
  15. 15.What is the value of 6⁻² (as a fraction)? =
  16. 16.Write 2.4 × 10⁻² as a decimal. =
  17. 17.What is the value of 3³ × 3⁻³? =
  18. 18.What is the value of 3¹ × 3⁻¹? =
  19. 19.What is the value of 3⁻³ (as a fraction)? =
  20. 20.What is the value of (8/9)⁻²? =
  21. 21.What is the value of 5⁴? =
  22. 22.What is the value of 10⁴ × 10⁻²? =
  23. 23.What is the value of 10¹ × 10⁻¹? =
  24. 24.Write 6² × 6² as a single power 6ⁿ. What is n?
  25. 25.What is the value of 3⁻⁴ (as a fraction)? =
  26. 26.What is the value of 6⁶? =
  27. 27.What is the value of 10⁻² (as a fraction)? =
  28. 28.Write 8.1 × 10⁻² as a decimal. =
  29. 29.Write 4.1 × 10⁻¹ as a decimal. =
  30. 30.Write 7.4 × 10⁻³ as a decimal. =
  31. 31.Write 1.7 × 10⁻¹ as a decimal. =
  32. 32.What is the value of 6⁻³ (as a fraction)? =
  33. 33.Write 6.5 × 10⁻¹ as a decimal. =
  34. 34.What is the value of 2⁻⁷ (as a fraction)? =
  35. 35.What is the value of 2¹⁴? =
  36. 36.What is the value of 2⁴ × 2⁻²? =
  37. 37.What is the value of 2⁵? =
  38. 38.Write 16,00,000 in standard form as 1.6 × 10ⁿ. What is n?
  39. 39.Write 4¹⁶ ÷ 4⁹ as a single power 4ⁿ. What is n?
  40. 40.What is the value of 2¹ × 2⁻²? =

Answer key

  1. 0.078
  2. 0.047
  3. 0.00063
  4. 1/5
  5. 1/8
  6. 9600000
  7. 10000
  8. 8/7
  9. 930000
  10. 100
  11. 2187
  12. 0.0053
  13. 4096
  14. 0.21
  15. 1/36
  16. 0.024
  17. 1
  18. 1
  19. 1/27
  20. 81/64
  21. 625
  22. 100
  23. 1
  24. 4
  25. 1/81
  26. 46656
  27. 1/100
  28. 0.081
  29. 0.41
  30. 0.0074
  31. 0.17
  32. 1/216
  33. 0.65
  34. 1/128
  35. 16384
  36. 4
  37. 32
  38. 6
  39. 7
  40. 1/2

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