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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 461 · 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 74,00,000 in standard form as 7.4 × 10ⁿ. What is n?
  2. 2.Write 43,000 in standard form as 4.3 × 10ⁿ. What is n?
  3. 3.What is the value of 3⁻⁵ (as a fraction)? =
  4. 4.Write (8⁵)³ as a single power 8ⁿ. What is n?
  5. 5.Write 3.4 × 10⁻³ as a decimal. =
  6. 6.Write 4.3 × 10⁻⁴ as a decimal. =
  7. 7.Write 6.9 × 10⁻⁴ as a decimal. =
  8. 8.What is the value of 2¹⁵? =
  9. 9.Write 3¹⁴ ÷ 3⁸ as a single power 3ⁿ. What is n?
  10. 10.Write 2,800 in standard form as 2.8 × 10ⁿ. What is n?
  11. 11.Write 9⁷ × 9⁴ as a single power 9ⁿ. What is n?
  12. 12.What is the value of 2⁴ × 2⁻⁵? =
  13. 13.Write 2.7 × 10⁻¹ as a decimal. =
  14. 14.What is the value of 3⁵ × 3⁻²? =
  15. 15.What is the value of 2¹⁰? =
  16. 16.Write 7¹⁰ ÷ 7⁶ as a single power 7ⁿ. What is n?
  17. 17.Write 7.5 × 10⁻¹ as a decimal. =
  18. 18.7.4 × 10⁶ =
  19. 19.What is the value of 10⁵ × 10⁻¹? =
  20. 20.What is the value of 8³? =
  21. 21.What is the value of 2⁶ × 2⁻⁴? =
  22. 22.Write 4⁶ × 4⁴ as a single power 4ⁿ. What is n?
  23. 23.Write 3.8 × 10⁻³ as a decimal. =
  24. 24.Write 9.4 × 10⁻³ as a decimal. =
  25. 25.What is the value of 2¹ × 2⁻¹? =
  26. 26.Write 6.6 × 10⁻¹ as a decimal. =
  27. 27.Write 7⁹ × 7⁴ as a single power 7ⁿ. What is n?
  28. 28.Write 8⁴ ÷ 8² as a single power 8ⁿ. What is n?
  29. 29.Write 4¹¹ ÷ 4⁶ as a single power 4ⁿ. What is n?
  30. 30.Write (2⁴)⁴ as a single power 2ⁿ. What is n?
  31. 31.Write 2 × 10⁻² as a decimal. =
  32. 32.Write 7¹⁶ ÷ 7⁹ as a single power 7ⁿ. What is n?
  33. 33.What is the value of (8/9)⁻²? =
  34. 34.Write 8⁷ × 8² as a single power 8ⁿ. What is n?
  35. 35.Write 5,600 in standard form as 5.6 × 10ⁿ. What is n?
  36. 36.What is the value of 5⁴? =
  37. 37.What is the value of 5⁴ × 5⁻²? =
  38. 38.Write 2,300 in standard form as 2.3 × 10ⁿ. What is n?
  39. 39.Write 8,20,000 in standard form as 8.2 × 10ⁿ. What is n?
  40. 40.Write 3.7 × 10⁻³ as a decimal. =

Answer key

  1. 6
  2. 4
  3. 1/243
  4. 15
  5. 0.0034
  6. 0.00043
  7. 0.00069
  8. 32768
  9. 6
  10. 3
  11. 11
  12. 1/2
  13. 0.27
  14. 27
  15. 1024
  16. 4
  17. 0.75
  18. 7400000
  19. 10000
  20. 512
  21. 4
  22. 10
  23. 0.0038
  24. 0.0094
  25. 1
  26. 0.66
  27. 13
  28. 2
  29. 5
  30. 16
  31. 0.02
  32. 7
  33. 81/64
  34. 9
  35. 3
  36. 625
  37. 25
  38. 3
  39. 5
  40. 0.0037

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