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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 127 · 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 9¹¹ ÷ 9⁸ as a single power 9ⁿ. What is n?
  2. 2.What is the value of 2¹³? =
  3. 3.What is the value of (5/8)⁻²? =
  4. 4.What is the value of 4³? =
  5. 5.Write 5⁸ × 5⁴ as a single power 5ⁿ. What is n?
  6. 6.What is the value of 7⁻² (as a fraction)? =
  7. 7.Write 7,500 in standard form as 7.5 × 10ⁿ. What is n?
  8. 8.What is the value of 2¹⁰? =
  9. 9.What is the value of 3³? =
  10. 10.Write 4⁷ × 4⁶ as a single power 4ⁿ. What is n?
  11. 11.Write 9 × 10⁻³ as a decimal. =
  12. 12.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  13. 13.7 × 10² =
  14. 14.What is the value of 5⁻² (as a fraction)? =
  15. 15.What is the value of 2¹⁶? =
  16. 16.Write 3² × 3² as a single power 3ⁿ. What is n?
  17. 17.What is the value of 2¹²? =
  18. 18.Write 2⁶ ÷ 2³ as a single power 2ⁿ. What is n?
  19. 19.Write 1.3 × 10⁻¹ as a decimal. =
  20. 20.Write 6¹² ÷ 6⁹ as a single power 6ⁿ. What is n?
  21. 21.What is the value of 8⁻³ (as a fraction)? =
  22. 22.Write 1.1 × 10⁻⁴ as a decimal. =
  23. 23.What is the value of (5/6)⁻¹? =
  24. 24.What is the value of (2/3)⁻¹? =
  25. 25.What is the value of (1/7)⁻²? =
  26. 26.What is the value of (3/8)⁻¹? =
  27. 27.Write 1.3 × 10⁻³ as a decimal. =
  28. 28.Write 9⁶ × 9⁴ as a single power 9ⁿ. What is n?
  29. 29.What is the value of 2⁻⁵ (as a fraction)? =
  30. 30.Write 6.6 × 10⁻⁴ as a decimal. =
  31. 31.Write 8⁴ × 8⁵ as a single power 8ⁿ. What is n?
  32. 32.What is the value of 2⁴? =
  33. 33.What is the value of (6/7)⁻²? =
  34. 34.Write (3³)⁷ as a single power 3ⁿ. What is n?
  35. 35.Write 5.4 × 10⁻³ as a decimal. =
  36. 36.Write (7⁵)⁵ as a single power 7ⁿ. What is n?
  37. 37.Write 75,000 in standard form as 7.5 × 10ⁿ. What is n?
  38. 38.Write (7⁵)² as a single power 7ⁿ. What is n?
  39. 39.What is the value of 2⁷? =
  40. 40.What is the value of (5/7)⁻²? =

Answer key

  1. 3
  2. 8192
  3. 64/25
  4. 64
  5. 12
  6. 1/49
  7. 3
  8. 1024
  9. 27
  10. 13
  11. 0.009
  12. 9
  13. 700
  14. 1/25
  15. 65536
  16. 4
  17. 4096
  18. 3
  19. 0.13
  20. 3
  21. 1/512
  22. 0.00011
  23. 6/5
  24. 3/2
  25. 49
  26. 8/3
  27. 0.0013
  28. 10
  29. 1/32
  30. 0.00066
  31. 9
  32. 16
  33. 49/36
  34. 21
  35. 0.0054
  36. 25
  37. 4
  38. 10
  39. 128
  40. 49/25

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