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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 764 · 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.What is the value of (7/8)⁻²? =
  2. 2.Write 3.9 × 10⁻² as a decimal. =
  3. 3.What is the value of (1/7)⁻²? =
  4. 4.What is the value of 3⁴ × 3⁻⁶? =
  5. 5.What is the value of 2⁻² (as a fraction)? =
  6. 6.What is the value of 9³? =
  7. 7.Write 8 × 10⁻⁴ as a decimal. =
  8. 8.Write 3.2 × 10⁻¹ as a decimal. =
  9. 9.Write 2.4 × 10⁻³ as a decimal. =
  10. 10.What is the value of (1/4)⁻¹? =
  11. 11.Write 8¹³ ÷ 8⁸ as a single power 8ⁿ. What is n?
  12. 12.Write 2,400 in standard form as 2.4 × 10ⁿ. What is n?
  13. 13.What is the value of 4⁶? =
  14. 14.Write 860 in standard form as 8.6 × 10ⁿ. What is n?
  15. 15.Write 2¹⁴ ÷ 2⁷ as a single power 2ⁿ. What is n?
  16. 16.What is the value of 2⁻⁵ (as a fraction)? =
  17. 17.What is the value of 5⁴ × 5⁻⁴? =
  18. 18.What is the value of 2⁻⁸ (as a fraction)? =
  19. 19.1.7 × 10⁷ =
  20. 20.What is the value of 10⁴ × 10⁻³? =
  21. 21.What is the value of 2⁴ × 2⁻³? =
  22. 22.What is the value of 2¹ × 2⁻⁵? =
  23. 23.Write 54,00,000 in standard form as 5.4 × 10ⁿ. What is n?
  24. 24.Write 4,100 in standard form as 4.1 × 10ⁿ. What is n?
  25. 25.What is the value of 7⁻¹ (as a fraction)? =
  26. 26.Write 1.5 × 10⁻¹ as a decimal. =
  27. 27.7.6 × 10⁷ =
  28. 28.What is the value of 8⁻³ (as a fraction)? =
  29. 29.Write 2.7 × 10⁻⁴ as a decimal. =
  30. 30.6.3 × 10³ =
  31. 31.What is the value of 10⁴ × 10⁻²? =
  32. 32.What is the value of 3⁶ × 3⁻²? =
  33. 33.Write 3⁹ × 3⁴ as a single power 3ⁿ. What is n?
  34. 34.What is the value of 2⁸? =
  35. 35.What is the value of 6⁻³ (as a fraction)? =
  36. 36.What is the value of 2⁴ × 2⁻²? =
  37. 37.Write 7² × 7⁶ as a single power 7ⁿ. What is n?
  38. 38.Write 8⁶ × 8⁷ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 2⁵ × 2⁻¹? =
  40. 40.Write 6⁶ × 6⁴ as a single power 6ⁿ. What is n?

Answer key

  1. 64/49
  2. 0.039
  3. 49
  4. 1/9
  5. 1/4
  6. 729
  7. 0.0008
  8. 0.32
  9. 0.0024
  10. 4
  11. 5
  12. 3
  13. 4096
  14. 2
  15. 7
  16. 1/32
  17. 1
  18. 1/256
  19. 17000000
  20. 10
  21. 2
  22. 1/16
  23. 6
  24. 3
  25. 1/7
  26. 0.15
  27. 76000000
  28. 1/512
  29. 0.00027
  30. 6300
  31. 100
  32. 81
  33. 13
  34. 256
  35. 1/216
  36. 4
  37. 8
  38. 13
  39. 16
  40. 10

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