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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 277 · 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 (5³)⁸ as a single power 5ⁿ. What is n?
  2. 2.What is the value of 6⁻³ (as a fraction)? =
  3. 3.Write 4⁸ × 4⁷ as a single power 4ⁿ. What is n?
  4. 4.Write (8²)⁶ as a single power 8ⁿ. What is n?
  5. 5.What is the value of (5/6)⁻²? =
  6. 6.What is the value of 9⁴? =
  7. 7.What is the value of (3/4)⁻²? =
  8. 8.Write (4⁹)⁶ as a single power 4ⁿ. What is n?
  9. 9.Write 9.4 × 10⁻¹ as a decimal. =
  10. 10.8.4 × 10⁷ =
  11. 11.Write (7⁷)⁷ as a single power 7ⁿ. What is n?
  12. 12.What is the value of 2⁻² (as a fraction)? =
  13. 13.What is the value of 3⁷? =
  14. 14.Write 7.4 × 10⁻² as a decimal. =
  15. 15.What is the value of 4⁴? =
  16. 16.Write 7⁶ ÷ 7³ as a single power 7ⁿ. What is n?
  17. 17.What is the value of 3⁻¹ (as a fraction)? =
  18. 18.What is the value of (1/3)⁻²? =
  19. 19.Write 6¹⁰ ÷ 6⁸ as a single power 6ⁿ. What is n?
  20. 20.Write 1.1 × 10⁻³ as a decimal. =
  21. 21.Write 5.2 × 10⁻² as a decimal. =
  22. 22.What is the value of 2⁶ × 2⁻³? =
  23. 23.Write 8,30,00,000 in standard form as 8.3 × 10ⁿ. What is n?
  24. 24.Write 5⁷ ÷ 5² as a single power 5ⁿ. What is n?
  25. 25.Write 97,000 in standard form as 9.7 × 10ⁿ. What is n?
  26. 26.Write 3.2 × 10⁻¹ as a decimal. =
  27. 27.2 × 10⁷ =
  28. 28.What is the value of 3⁶? =
  29. 29.Write 2⁸ × 2² as a single power 2ⁿ. What is n?
  30. 30.What is the value of 2¹²? =
  31. 31.What is the value of 9⁻² (as a fraction)? =
  32. 32.3.5 × 10³ =
  33. 33.Write 6⁹ × 6⁶ as a single power 6ⁿ. What is n?
  34. 34.7.2 × 10⁴ =
  35. 35.What is the value of 3⁶ × 3⁻⁵? =
  36. 36.Write 9.2 × 10⁻¹ as a decimal. =
  37. 37.What is the value of 2³? =
  38. 38.2.4 × 10³ =
  39. 39.Write 3,50,000 in standard form as 3.5 × 10ⁿ. What is n?
  40. 40.What is the value of 2¹⁴? =

Answer key

  1. 24
  2. 1/216
  3. 15
  4. 12
  5. 36/25
  6. 6561
  7. 16/9
  8. 54
  9. 0.94
  10. 84000000
  11. 49
  12. 1/4
  13. 2187
  14. 0.074
  15. 256
  16. 3
  17. 1/3
  18. 9
  19. 2
  20. 0.0011
  21. 0.052
  22. 8
  23. 7
  24. 5
  25. 4
  26. 0.32
  27. 20000000
  28. 729
  29. 10
  30. 4096
  31. 1/81
  32. 3500
  33. 15
  34. 72000
  35. 3
  36. 0.92
  37. 8
  38. 2400
  39. 5
  40. 16384

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