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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 861 · 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 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  2. 2.What is the value of 2⁻¹ (as a fraction)? =
  3. 3.What is the value of 4⁷? =
  4. 4.What is the value of (3/5)⁻²? =
  5. 5.What is the value of 2¹¹? =
  6. 6.What is the value of 7³? =
  7. 7.Write 5.5 × 10⁻¹ as a decimal. =
  8. 8.What is the value of 5⁶ × 5⁻¹? =
  9. 9.What is the value of 5⁷? =
  10. 10.3.3 × 10⁴ =
  11. 11.What is the value of 2²? =
  12. 12.What is the value of 10⁻³ (as a fraction)? =
  13. 13.What is the value of 8⁻¹ (as a fraction)? =
  14. 14.Write 6,20,00,000 in standard form as 6.2 × 10ⁿ. What is n?
  15. 15.What is the value of 10³ × 10⁻²? =
  16. 16.What is the value of (8/9)⁻²? =
  17. 17.Write 6⁵ × 6⁷ as a single power 6ⁿ. What is n?
  18. 18.What is the value of 4⁸? =
  19. 19.Write 150 in standard form as 1.5 × 10ⁿ. What is n?
  20. 20.What is the value of 2⁹? =
  21. 21.Write 7.4 × 10⁻¹ as a decimal. =
  22. 22.Write 30,000 in standard form as 3 × 10ⁿ. What is n?
  23. 23.What is the value of 5¹ × 5⁻³? =
  24. 24.Write 3 × 10⁻¹ as a decimal. =
  25. 25.Write 92,00,000 in standard form as 9.2 × 10ⁿ. What is n?
  26. 26.What is the value of 10⁻¹ (as a fraction)? =
  27. 27.Write 57,00,000 in standard form as 5.7 × 10ⁿ. What is n?
  28. 28.Write 1,30,00,000 in standard form as 1.3 × 10ⁿ. What is n?
  29. 29.Write 1.2 × 10⁻² as a decimal. =
  30. 30.Write 7.5 × 10⁻¹ as a decimal. =
  31. 31.What is the value of 2⁶ × 2⁻²? =
  32. 32.Write 5.8 × 10⁻⁴ as a decimal. =
  33. 33.Write 7.6 × 10⁻² as a decimal. =
  34. 34.Write 1.9 × 10⁻⁴ as a decimal. =
  35. 35.What is the value of 3⁸? =
  36. 36.What is the value of 3¹ × 3⁻³? =
  37. 37.Write 3³ × 3⁵ as a single power 3ⁿ. What is n?
  38. 38.1.9 × 10⁷ =
  39. 39.Write 5⁹ × 5⁴ as a single power 5ⁿ. What is n?
  40. 40.What is the value of 10³? =

Answer key

  1. 3
  2. 1/2
  3. 16384
  4. 25/9
  5. 2048
  6. 343
  7. 0.55
  8. 3125
  9. 78125
  10. 33000
  11. 4
  12. 1/1000
  13. 1/8
  14. 7
  15. 10
  16. 81/64
  17. 12
  18. 65536
  19. 2
  20. 512
  21. 0.74
  22. 4
  23. 1/25
  24. 0.3
  25. 6
  26. 1/10
  27. 6
  28. 7
  29. 0.012
  30. 0.75
  31. 16
  32. 0.00058
  33. 0.076
  34. 0.00019
  35. 6561
  36. 1/9
  37. 8
  38. 19000000
  39. 13
  40. 1000

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