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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 741 · 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 8² × 8³ as a single power 8ⁿ. What is n?
  2. 2.What is the value of 2⁵ × 2⁻³? =
  3. 3.What is the value of 2⁵? =
  4. 4.Write 2³ × 2⁵ as a single power 2ⁿ. What is n?
  5. 5.Write 6⁵ × 6⁶ as a single power 6ⁿ. What is n?
  6. 6.What is the value of 3⁴ × 3⁻³? =
  7. 7.What is the value of 2⁴ × 2⁻¹? =
  8. 8.What is the value of 3³ × 3⁻³? =
  9. 9.What is the value of 9²? =
  10. 10.What is the value of 8⁻³ (as a fraction)? =
  11. 11.Write 5.2 × 10⁻³ as a decimal. =
  12. 12.What is the value of 2⁷? =
  13. 13.What is the value of 7⁻³ (as a fraction)? =
  14. 14.What is the value of 10⁴ × 10⁻⁴? =
  15. 15.Write 7,80,000 in standard form as 7.8 × 10ⁿ. What is n?
  16. 16.Write 77,000 in standard form as 7.7 × 10ⁿ. What is n?
  17. 17.Write (2³)⁶ as a single power 2ⁿ. What is n?
  18. 18.Write 2.8 × 10⁻¹ as a decimal. =
  19. 19.Write 9.5 × 10⁻⁴ as a decimal. =
  20. 20.What is the value of 10⁶ × 10⁻⁴? =
  21. 21.What is the value of 2² × 2⁻⁵? =
  22. 22.7.1 × 10³ =
  23. 23.What is the value of 3⁴ × 3⁻⁶? =
  24. 24.Write 2.6 × 10⁻¹ as a decimal. =
  25. 25.2.7 × 10³ =
  26. 26.Write 6.5 × 10⁻¹ as a decimal. =
  27. 27.Write 5,10,00,000 in standard form as 5.1 × 10ⁿ. What is n?
  28. 28.Write 87,000 in standard form as 8.7 × 10ⁿ. What is n?
  29. 29.What is the value of 3² × 3⁻⁵? =
  30. 30.Write 8.6 × 10⁻¹ as a decimal. =
  31. 31.What is the value of 2¹⁵? =
  32. 32.What is the value of 5²? =
  33. 33.What is the value of (2/5)⁻¹? =
  34. 34.What is the value of 3⁶? =
  35. 35.Write 1,700 in standard form as 1.7 × 10ⁿ. What is n?
  36. 36.What is the value of (1/5)⁻²? =
  37. 37.Write 8 × 10⁻³ as a decimal. =
  38. 38.9.7 × 10² =
  39. 39.Write 4.1 × 10⁻¹ as a decimal. =
  40. 40.Write 3⁷ × 3⁸ as a single power 3ⁿ. What is n?

Answer key

  1. 5
  2. 4
  3. 32
  4. 8
  5. 11
  6. 3
  7. 8
  8. 1
  9. 81
  10. 1/512
  11. 0.0052
  12. 128
  13. 1/343
  14. 1
  15. 5
  16. 4
  17. 18
  18. 0.28
  19. 0.00095
  20. 100
  21. 1/8
  22. 7100
  23. 1/9
  24. 0.26
  25. 2700
  26. 0.65
  27. 7
  28. 4
  29. 1/27
  30. 0.86
  31. 32768
  32. 25
  33. 5/2
  34. 729
  35. 3
  36. 25
  37. 0.008
  38. 970
  39. 0.41
  40. 15

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