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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 748 · 40 sums
TalentJR

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 3⁻¹ (as a fraction)? =
  2. 2.What is the value of 6²? =
  3. 3.1.8 × 10³ =
  4. 4.What is the value of 5² × 5⁻⁴? =
  5. 5.What is the value of 10⁴ × 10⁻⁶? =
  6. 6.Write 5³ × 5² as a single power 5ⁿ. What is n?
  7. 7.What is the value of (1/6)⁻²? =
  8. 8.What is the value of 3² × 3⁻¹? =
  9. 9.Write 3,700 in standard form as 3.7 × 10ⁿ. What is n?
  10. 10.What is the value of (1/2)⁻²? =
  11. 11.Write 6¹² ÷ 6³ as a single power 6ⁿ. What is n?
  12. 12.What is the value of 3⁶? =
  13. 13.Write 2 × 10⁻⁴ as a decimal. =
  14. 14.8 × 10⁷ =
  15. 15.What is the value of 2² × 2⁻¹? =
  16. 16.Write 4⁸ ÷ 4² as a single power 4ⁿ. What is n?
  17. 17.What is the value of 7⁻² (as a fraction)? =
  18. 18.What is the value of 3⁻⁴ (as a fraction)? =
  19. 19.What is the value of 3⁻⁶ (as a fraction)? =
  20. 20.What is the value of 9⁻² (as a fraction)? =
  21. 21.What is the value of 3³ × 3⁻³? =
  22. 22.Write 61,000 in standard form as 6.1 × 10ⁿ. What is n?
  23. 23.What is the value of 9⁵? =
  24. 24.Write 2⁹ × 2⁵ as a single power 2ⁿ. What is n?
  25. 25.What is the value of 2⁻³ (as a fraction)? =
  26. 26.What is the value of 6⁻¹ (as a fraction)? =
  27. 27.Write 1.2 × 10⁻¹ as a decimal. =
  28. 28.What is the value of 6⁴? =
  29. 29.7.1 × 10⁷ =
  30. 30.Write 2.6 × 10⁻¹ as a decimal. =
  31. 31.What is the value of 5⁻¹ (as a fraction)? =
  32. 32.What is the value of 6⁻² (as a fraction)? =
  33. 33.What is the value of 10⁶ × 10⁻³? =
  34. 34.What is the value of 5⁻³ (as a fraction)? =
  35. 35.Write (4³)⁶ as a single power 4ⁿ. What is n?
  36. 36.What is the value of 9³? =
  37. 37.9 × 10² =
  38. 38.3.7 × 10⁵ =
  39. 39.What is the value of 2⁻⁵ (as a fraction)? =
  40. 40.Write (8⁷)⁷ as a single power 8ⁿ. What is n?

Answer key

  1. 1/3
  2. 36
  3. 1800
  4. 1/25
  5. 1/100
  6. 5
  7. 36
  8. 3
  9. 3
  10. 4
  11. 9
  12. 729
  13. 0.0002
  14. 80000000
  15. 2
  16. 6
  17. 1/49
  18. 1/81
  19. 1/729
  20. 1/81
  21. 1
  22. 4
  23. 59049
  24. 14
  25. 1/8
  26. 1/6
  27. 0.12
  28. 1296
  29. 71000000
  30. 0.26
  31. 1/5
  32. 1/36
  33. 1000
  34. 1/125
  35. 18
  36. 729
  37. 900
  38. 370000
  39. 1/32
  40. 49

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