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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 117 · 40 sums
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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 4¹⁷ ÷ 4⁸ as a single power 4ⁿ. What is n?
  2. 2.Write 3.5 × 10⁻¹ as a decimal. =
  3. 3.Write 3.7 × 10⁻² as a decimal. =
  4. 4.What is the value of 5⁴ × 5⁻⁴? =
  5. 5.What is the value of 8⁴? =
  6. 6.What is the value of 5¹ × 5⁻³? =
  7. 7.Write 2,60,00,000 in standard form as 2.6 × 10ⁿ. What is n?
  8. 8.Write 96,00,000 in standard form as 9.6 × 10ⁿ. What is n?
  9. 9.What is the value of 10¹ × 10⁻⁵? =
  10. 10.Write 4,700 in standard form as 4.7 × 10ⁿ. What is n?
  11. 11.Write 1.4 × 10⁻³ as a decimal. =
  12. 12.Write (3²)² as a single power 3ⁿ. What is n?
  13. 13.Write 62,00,000 in standard form as 6.2 × 10ⁿ. What is n?
  14. 14.Write 3.6 × 10⁻¹ as a decimal. =
  15. 15.Write 2,70,00,000 in standard form as 2.7 × 10ⁿ. What is n?
  16. 16.Write (8⁸)² as a single power 8ⁿ. What is n?
  17. 17.What is the value of 2⁻² (as a fraction)? =
  18. 18.Write 2.5 × 10⁻² as a decimal. =
  19. 19.Write 6¹⁶ ÷ 6⁹ as a single power 6ⁿ. What is n?
  20. 20.Write 2.6 × 10⁻² as a decimal. =
  21. 21.Write (4⁹)⁸ as a single power 4ⁿ. What is n?
  22. 22.Write 2⁷ × 2⁵ as a single power 2ⁿ. What is n?
  23. 23.What is the value of 5³ × 5⁻⁶? =
  24. 24.Write 7⁵ ÷ 7³ as a single power 7ⁿ. What is n?
  25. 25.Write 9.5 × 10⁻² as a decimal. =
  26. 26.Write 40,00,000 in standard form as 4 × 10ⁿ. What is n?
  27. 27.Write 5² × 5⁸ as a single power 5ⁿ. What is n?
  28. 28.Write 9² × 9⁶ as a single power 9ⁿ. What is n?
  29. 29.What is the value of 2⁻³ (as a fraction)? =
  30. 30.What is the value of (1/5)⁻²? =
  31. 31.Write 9⁶ × 9⁴ as a single power 9ⁿ. What is n?
  32. 32.Write 4¹³ ÷ 4⁸ as a single power 4ⁿ. What is n?
  33. 33.7.4 × 10³ =
  34. 34.Write 8.7 × 10⁻³ as a decimal. =
  35. 35.Write (3⁹)⁶ as a single power 3ⁿ. What is n?
  36. 36.Write 6³ × 6⁶ as a single power 6ⁿ. What is n?
  37. 37.What is the value of 2¹⁵? =
  38. 38.What is the value of 8⁵? =
  39. 39.Write 1.2 × 10⁻² as a decimal. =
  40. 40.Write 2.2 × 10⁻² as a decimal. =

Answer key

  1. 9
  2. 0.35
  3. 0.037
  4. 1
  5. 4096
  6. 1/25
  7. 7
  8. 6
  9. 1/10000
  10. 3
  11. 0.0014
  12. 4
  13. 6
  14. 0.36
  15. 7
  16. 16
  17. 1/4
  18. 0.025
  19. 7
  20. 0.026
  21. 72
  22. 12
  23. 1/125
  24. 2
  25. 0.095
  26. 6
  27. 10
  28. 8
  29. 1/8
  30. 25
  31. 10
  32. 5
  33. 7400
  34. 0.0087
  35. 54
  36. 9
  37. 32768
  38. 32768
  39. 0.012
  40. 0.022

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