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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 10 · 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.What is the value of 5⁻⁴ (as a fraction)? =
  2. 2.Write 5,70,000 in standard form as 5.7 × 10ⁿ. What is n?
  3. 3.What is the value of 5⁶ × 5⁻⁶? =
  4. 4.Write 6⁴ × 6² as a single power 6ⁿ. What is n?
  5. 5.What is the value of 5⁴ × 5⁻²? =
  6. 6.Write 2⁴ × 2⁹ as a single power 2ⁿ. What is n?
  7. 7.What is the value of (2/7)⁻²? =
  8. 8.What is the value of 3³ × 3⁻⁶? =
  9. 9.What is the value of 3⁻¹ (as a fraction)? =
  10. 10.What is the value of 2⁶? =
  11. 11.Write 1.2 × 10⁻² as a decimal. =
  12. 12.What is the value of 4⁻¹ (as a fraction)? =
  13. 13.What is the value of 4²? =
  14. 14.Write 7,10,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  15. 15.Write 9³ × 9² as a single power 9ⁿ. What is n?
  16. 16.Write 2⁴ × 2⁶ as a single power 2ⁿ. What is n?
  17. 17.What is the value of (4/7)⁻²? =
  18. 18.What is the value of (1/5)⁻¹? =
  19. 19.What is the value of 9⁻³ (as a fraction)? =
  20. 20.What is the value of 2⁻⁷ (as a fraction)? =
  21. 21.What is the value of 9⁻² (as a fraction)? =
  22. 22.What is the value of 5⁻³ (as a fraction)? =
  23. 23.What is the value of 2⁻⁹ (as a fraction)? =
  24. 24.5.2 × 10³ =
  25. 25.Write (9³)³ as a single power 9ⁿ. What is n?
  26. 26.7.7 × 10² =
  27. 27.Write 2¹⁶ ÷ 2⁷ as a single power 2ⁿ. What is n?
  28. 28.Write 6¹¹ ÷ 6⁸ as a single power 6ⁿ. What is n?
  29. 29.Write 2.3 × 10⁻² as a decimal. =
  30. 30.What is the value of (1/3)⁻¹? =
  31. 31.What is the value of 5⁵ × 5⁻⁶? =
  32. 32.What is the value of 2¹³? =
  33. 33.What is the value of 5⁴? =
  34. 34.What is the value of 2¹¹? =
  35. 35.Write 5,700 in standard form as 5.7 × 10ⁿ. What is n?
  36. 36.What is the value of 3⁶ × 3⁻⁴? =
  37. 37.What is the value of 10³ × 10⁻⁶? =
  38. 38.What is the value of 3¹ × 3⁻²? =
  39. 39.Write 2⁹ × 2² as a single power 2ⁿ. What is n?
  40. 40.Write 170 in standard form as 1.7 × 10ⁿ. What is n?

Answer key

  1. 1/625
  2. 5
  3. 1
  4. 6
  5. 25
  6. 13
  7. 49/4
  8. 1/27
  9. 1/3
  10. 64
  11. 0.012
  12. 1/4
  13. 16
  14. 7
  15. 5
  16. 10
  17. 49/16
  18. 5
  19. 1/729
  20. 1/128
  21. 1/81
  22. 1/125
  23. 1/512
  24. 5200
  25. 9
  26. 770
  27. 9
  28. 3
  29. 0.023
  30. 3
  31. 1/5
  32. 8192
  33. 625
  34. 2048
  35. 3
  36. 9
  37. 1/1000
  38. 1/3
  39. 11
  40. 2

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