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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 4 · 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 18,000 in standard form as 1.8 × 10ⁿ. What is n?
  2. 2.What is the value of 3⁶ × 3⁻⁴? =
  3. 3.Write 3.4 × 10⁻¹ as a decimal. =
  4. 4.Write 8.8 × 10⁻³ as a decimal. =
  5. 5.Write 170 in standard form as 1.7 × 10ⁿ. What is n?
  6. 6.What is the value of 2¹ × 2⁻⁵? =
  7. 7.What is the value of 6³? =
  8. 8.What is the value of 2¹³? =
  9. 9.What is the value of 3⁷? =
  10. 10.Write 860 in standard form as 8.6 × 10ⁿ. What is n?
  11. 11.Write 9.8 × 10⁻² as a decimal. =
  12. 12.Write 4.9 × 10⁻² as a decimal. =
  13. 13.Write 6,60,00,000 in standard form as 6.6 × 10ⁿ. What is n?
  14. 14.Write (4²)⁵ as a single power 4ⁿ. What is n?
  15. 15.Write 2.7 × 10⁻¹ as a decimal. =
  16. 16.Write 9⁵ × 9⁴ as a single power 9ⁿ. What is n?
  17. 17.Write 6¹³ ÷ 6⁶ as a single power 6ⁿ. What is n?
  18. 18.What is the value of (3/7)⁻¹? =
  19. 19.What is the value of 3⁵? =
  20. 20.Write 8⁴ × 8⁷ as a single power 8ⁿ. What is n?
  21. 21.What is the value of (3/5)⁻²? =
  22. 22.What is the value of 10¹ × 10⁻³? =
  23. 23.What is the value of 2⁴? =
  24. 24.What is the value of 8⁵? =
  25. 25.Write 240 in standard form as 2.4 × 10ⁿ. What is n?
  26. 26.Write 7.5 × 10⁻¹ as a decimal. =
  27. 27.Write 4.5 × 10⁻³ as a decimal. =
  28. 28.Write 5⁶ × 5³ as a single power 5ⁿ. What is n?
  29. 29.2.3 × 10³ =
  30. 30.What is the value of 7⁻¹ (as a fraction)? =
  31. 31.Write 5.4 × 10⁻¹ as a decimal. =
  32. 32.Write 9.8 × 10⁻⁴ as a decimal. =
  33. 33.Write (6⁹)⁹ as a single power 6ⁿ. What is n?
  34. 34.What is the value of 5⁵? =
  35. 35.What is the value of 2¹⁴? =
  36. 36.What is the value of 4⁻² (as a fraction)? =
  37. 37.What is the value of 2¹ × 2⁻¹? =
  38. 38.What is the value of 3⁶ × 3⁻⁶? =
  39. 39.What is the value of 2²? =
  40. 40.What is the value of 2⁵ × 2⁻⁶? =

Answer key

  1. 4
  2. 9
  3. 0.34
  4. 0.0088
  5. 2
  6. 1/16
  7. 216
  8. 8192
  9. 2187
  10. 2
  11. 0.098
  12. 0.049
  13. 7
  14. 10
  15. 0.27
  16. 9
  17. 7
  18. 7/3
  19. 243
  20. 11
  21. 25/9
  22. 1/100
  23. 16
  24. 32768
  25. 2
  26. 0.75
  27. 0.0045
  28. 9
  29. 2300
  30. 1/7
  31. 0.54
  32. 0.00098
  33. 81
  34. 3125
  35. 16384
  36. 1/16
  37. 1
  38. 1
  39. 4
  40. 1/2

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