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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 111 · 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 8⁸ ÷ 8² as a single power 8ⁿ. What is n?
  2. 2.What is the value of 6³? =
  3. 3.Write 2¹⁵ ÷ 2⁶ as a single power 2ⁿ. What is n?
  4. 4.3.9 × 10³ =
  5. 5.Write 7,700 in standard form as 7.7 × 10ⁿ. What is n?
  6. 6.Write 4.2 × 10⁻² as a decimal. =
  7. 7.Write 5.5 × 10⁻² as a decimal. =
  8. 8.What is the value of 3³ × 3⁻¹? =
  9. 9.What is the value of 2⁶ × 2⁻⁵? =
  10. 10.5.2 × 10⁵ =
  11. 11.Write 6¹³ ÷ 6⁹ as a single power 6ⁿ. What is n?
  12. 12.What is the value of 2⁻⁵ (as a fraction)? =
  13. 13.What is the value of (2/3)⁻²? =
  14. 14.What is the value of 5⁵ × 5⁻⁴? =
  15. 15.What is the value of 2⁶? =
  16. 16.Write 7.8 × 10⁻¹ as a decimal. =
  17. 17.What is the value of 3³ × 3⁻⁴? =
  18. 18.Write 6.8 × 10⁻¹ as a decimal. =
  19. 19.What is the value of 3⁴ × 3⁻⁵? =
  20. 20.What is the value of 3¹ × 3⁻²? =
  21. 21.Write 3.9 × 10⁻¹ as a decimal. =
  22. 22.What is the value of 3⁵? =
  23. 23.What is the value of 2⁴? =
  24. 24.Write 27,000 in standard form as 2.7 × 10ⁿ. What is n?
  25. 25.Write 3,600 in standard form as 3.6 × 10ⁿ. What is n?
  26. 26.2.5 × 10⁷ =
  27. 27.Write 3.1 × 10⁻³ as a decimal. =
  28. 28.5.3 × 10⁶ =
  29. 29.What is the value of 3² × 3⁻⁶? =
  30. 30.Write 5.8 × 10⁻¹ as a decimal. =
  31. 31.What is the value of (1/8)⁻¹? =
  32. 32.4.8 × 10⁵ =
  33. 33.Write 3,20,00,000 in standard form as 3.2 × 10ⁿ. What is n?
  34. 34.Write 8³ × 8⁸ as a single power 8ⁿ. What is n?
  35. 35.What is the value of 10⁵ × 10⁻²? =
  36. 36.Write 1.2 × 10⁻³ as a decimal. =
  37. 37.Write 3.1 × 10⁻¹ as a decimal. =
  38. 38.What is the value of 2⁵ × 2⁻³? =
  39. 39.What is the value of 4³? =
  40. 40.What is the value of (3/5)⁻¹? =

Answer key

  1. 6
  2. 216
  3. 9
  4. 3900
  5. 3
  6. 0.042
  7. 0.055
  8. 9
  9. 2
  10. 520000
  11. 4
  12. 1/32
  13. 9/4
  14. 5
  15. 64
  16. 0.78
  17. 1/3
  18. 0.68
  19. 1/3
  20. 1/3
  21. 0.39
  22. 243
  23. 16
  24. 4
  25. 3
  26. 25000000
  27. 0.0031
  28. 5300000
  29. 1/81
  30. 0.58
  31. 8
  32. 480000
  33. 7
  34. 11
  35. 1000
  36. 0.0012
  37. 0.31
  38. 4
  39. 64
  40. 5/3

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