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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 677 · 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.Write 9² × 9⁴ as a single power 9ⁿ. What is n?
  2. 2.Write 8¹⁰ ÷ 8² as a single power 8ⁿ. What is n?
  3. 3.What is the value of 7⁻¹ (as a fraction)? =
  4. 4.What is the value of 8³? =
  5. 5.Write 6.7 × 10⁻¹ as a decimal. =
  6. 6.What is the value of (6/7)⁻²? =
  7. 7.What is the value of 6⁴? =
  8. 8.What is the value of 2² × 2⁻⁵? =
  9. 9.Write 6.9 × 10⁻² as a decimal. =
  10. 10.What is the value of 2¹⁶? =
  11. 11.Write 75,000 in standard form as 7.5 × 10ⁿ. What is n?
  12. 12.Write 73,000 in standard form as 7.3 × 10ⁿ. What is n?
  13. 13.What is the value of 2⁵ × 2⁻²? =
  14. 14.What is the value of 10¹ × 10⁻⁴? =
  15. 15.What is the value of 3⁻¹ (as a fraction)? =
  16. 16.What is the value of 3³? =
  17. 17.What is the value of 10² × 10⁻⁵? =
  18. 18.What is the value of 8⁵? =
  19. 19.What is the value of (5/7)⁻²? =
  20. 20.3.2 × 10⁴ =
  21. 21.Write 8.2 × 10⁻⁴ as a decimal. =
  22. 22.Write 3⁸ ÷ 3² as a single power 3ⁿ. What is n?
  23. 23.Write 4⁹ × 4⁵ as a single power 4ⁿ. What is n?
  24. 24.What is the value of 2⁵ × 2⁻⁴? =
  25. 25.What is the value of 10⁻¹ (as a fraction)? =
  26. 26.Write 2.5 × 10⁻¹ as a decimal. =
  27. 27.Write 4,50,000 in standard form as 4.5 × 10ⁿ. What is n?
  28. 28.Write 9¹⁵ ÷ 9⁶ as a single power 9ⁿ. What is n?
  29. 29.Write 4.3 × 10⁻² as a decimal. =
  30. 30.9.9 × 10² =
  31. 31.What is the value of 2² × 2⁻²? =
  32. 32.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  33. 33.Write 2,100 in standard form as 2.1 × 10ⁿ. What is n?
  34. 34.What is the value of 4⁻³ (as a fraction)? =
  35. 35.What is the value of 4⁴? =
  36. 36.What is the value of (1/9)⁻¹? =
  37. 37.Write 8⁶ × 8⁷ as a single power 8ⁿ. What is n?
  38. 38.What is the value of 10³ × 10⁻⁶? =
  39. 39.3.6 × 10² =
  40. 40.What is the value of (2/7)⁻²? =

Answer key

  1. 6
  2. 8
  3. 1/7
  4. 512
  5. 0.67
  6. 49/36
  7. 1296
  8. 1/8
  9. 0.069
  10. 65536
  11. 4
  12. 4
  13. 8
  14. 1/1000
  15. 1/3
  16. 27
  17. 1/1000
  18. 32768
  19. 49/25
  20. 32000
  21. 0.00082
  22. 6
  23. 14
  24. 2
  25. 1/10
  26. 0.25
  27. 5
  28. 9
  29. 0.043
  30. 990
  31. 1
  32. 9
  33. 3
  34. 1/64
  35. 256
  36. 9
  37. 13
  38. 1/1000
  39. 360
  40. 49/4

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