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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 604 · 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 9⁻³ (as a fraction)? =
  2. 2.Write 87,00,000 in standard form as 8.7 × 10ⁿ. What is n?
  3. 3.Write 6⁸ × 6⁸ as a single power 6ⁿ. What is n?
  4. 4.Write 7⁹ ÷ 7⁵ as a single power 7ⁿ. What is n?
  5. 5.9.7 × 10³ =
  6. 6.Write 2.5 × 10⁻¹ as a decimal. =
  7. 7.What is the value of (7/9)⁻¹? =
  8. 8.What is the value of 2⁻⁹ (as a fraction)? =
  9. 9.7.7 × 10³ =
  10. 10.Write 8¹¹ ÷ 8⁸ as a single power 8ⁿ. What is n?
  11. 11.Write 6.7 × 10⁻¹ as a decimal. =
  12. 12.What is the value of 2¹²? =
  13. 13.Write (3⁷)² as a single power 3ⁿ. What is n?
  14. 14.Write (7⁵)⁶ as a single power 7ⁿ. What is n?
  15. 15.What is the value of 8³? =
  16. 16.Write 2.6 × 10⁻² as a decimal. =
  17. 17.What is the value of 3⁻² (as a fraction)? =
  18. 18.What is the value of 5⁻² (as a fraction)? =
  19. 19.Write 2⁹ ÷ 2⁷ as a single power 2ⁿ. What is n?
  20. 20.Write (9²)⁶ as a single power 9ⁿ. What is n?
  21. 21.What is the value of (1/8)⁻²? =
  22. 22.What is the value of (3/4)⁻¹? =
  23. 23.Write 2⁶ ÷ 2⁴ as a single power 2ⁿ. What is n?
  24. 24.What is the value of 8²? =
  25. 25.Write 49,000 in standard form as 4.9 × 10ⁿ. What is n?
  26. 26.What is the value of 3³ × 3⁻⁴? =
  27. 27.What is the value of 5⁴ × 5⁻⁵? =
  28. 28.Write 3 × 10⁻⁴ as a decimal. =
  29. 29.What is the value of 4⁻¹ (as a fraction)? =
  30. 30.What is the value of 5⁵ × 5⁻⁴? =
  31. 31.What is the value of 10⁵? =
  32. 32.What is the value of 3² × 3⁻⁶? =
  33. 33.What is the value of 5⁵ × 5⁻⁶? =
  34. 34.1.6 × 10⁴ =
  35. 35.9.6 × 10⁶ =
  36. 36.Write 9.7 × 10⁻³ as a decimal. =
  37. 37.What is the value of (1/8)⁻¹? =
  38. 38.Write 6¹² ÷ 6⁹ as a single power 6ⁿ. What is n?
  39. 39.Write 3 × 10⁻² as a decimal. =
  40. 40.What is the value of (3/5)⁻²? =

Answer key

  1. 1/729
  2. 6
  3. 16
  4. 4
  5. 9700
  6. 0.25
  7. 9/7
  8. 1/512
  9. 7700
  10. 3
  11. 0.67
  12. 4096
  13. 14
  14. 30
  15. 512
  16. 0.026
  17. 1/9
  18. 1/25
  19. 2
  20. 12
  21. 64
  22. 4/3
  23. 2
  24. 64
  25. 4
  26. 1/3
  27. 1/5
  28. 0.0003
  29. 1/4
  30. 5
  31. 100000
  32. 1/81
  33. 1/5
  34. 16000
  35. 9600000
  36. 0.0097
  37. 8
  38. 3
  39. 0.03
  40. 25/9

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