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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 74 · 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 3.4 × 10⁻¹ as a decimal. =
  2. 2.What is the value of 2¹ × 2⁻⁶? =
  3. 3.What is the value of 8²? =
  4. 4.What is the value of 10⁶ × 10⁻⁴? =
  5. 5.What is the value of 3¹⁰? =
  6. 6.Write 8³ × 8³ as a single power 8ⁿ. What is n?
  7. 7.Write 4.6 × 10⁻³ as a decimal. =
  8. 8.What is the value of 2⁴ × 2⁻²? =
  9. 9.What is the value of (3/5)⁻¹? =
  10. 10.Write 8² × 8³ as a single power 8ⁿ. What is n?
  11. 11.What is the value of 10⁴ × 10⁻²? =
  12. 12.What is the value of 3⁻¹ (as a fraction)? =
  13. 13.Write 6.8 × 10⁻² as a decimal. =
  14. 14.What is the value of 3² × 3⁻¹? =
  15. 15.What is the value of 5⁻⁴ (as a fraction)? =
  16. 16.5.9 × 10⁵ =
  17. 17.What is the value of 5³ × 5⁻¹? =
  18. 18.What is the value of 7³? =
  19. 19.What is the value of (7/9)⁻¹? =
  20. 20.Write 8² × 8⁸ as a single power 8ⁿ. What is n?
  21. 21.What is the value of (5/7)⁻²? =
  22. 22.Write 3³ × 3² as a single power 3ⁿ. What is n?
  23. 23.What is the value of 5³ × 5⁻³? =
  24. 24.What is the value of 5⁴? =
  25. 25.What is the value of 2⁵ × 2⁻⁶? =
  26. 26.What is the value of 6⁵? =
  27. 27.Write 6 × 10⁻² as a decimal. =
  28. 28.Write 6⁹ ÷ 6² as a single power 6ⁿ. What is n?
  29. 29.Write (9⁵)³ as a single power 9ⁿ. What is n?
  30. 30.Write 5¹⁰ ÷ 5³ as a single power 5ⁿ. What is n?
  31. 31.What is the value of 2¹²? =
  32. 32.Write 7¹¹ ÷ 7⁹ as a single power 7ⁿ. What is n?
  33. 33.What is the value of 9⁵? =
  34. 34.What is the value of 2⁻² (as a fraction)? =
  35. 35.What is the value of (7/9)⁻²? =
  36. 36.Write 1.7 × 10⁻³ as a decimal. =
  37. 37.Write (2³)⁵ as a single power 2ⁿ. What is n?
  38. 38.What is the value of 2¹ × 2⁻⁴? =
  39. 39.Write 26,000 in standard form as 2.6 × 10ⁿ. What is n?
  40. 40.8.5 × 10⁵ =

Answer key

  1. 0.34
  2. 1/32
  3. 64
  4. 100
  5. 59049
  6. 6
  7. 0.0046
  8. 4
  9. 5/3
  10. 5
  11. 100
  12. 1/3
  13. 0.068
  14. 3
  15. 1/625
  16. 590000
  17. 25
  18. 343
  19. 9/7
  20. 10
  21. 49/25
  22. 5
  23. 1
  24. 625
  25. 1/2
  26. 7776
  27. 0.06
  28. 7
  29. 15
  30. 7
  31. 4096
  32. 2
  33. 59049
  34. 1/4
  35. 81/49
  36. 0.0017
  37. 15
  38. 1/8
  39. 4
  40. 850000

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