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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 642 · 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 3⁻⁴ (as a fraction)? =
  2. 2.What is the value of (5/9)⁻¹? =
  3. 3.What is the value of 3⁸? =
  4. 4.Write 2¹² ÷ 2³ as a single power 2ⁿ. What is n?
  5. 5.2.6 × 10⁶ =
  6. 6.What is the value of 7⁻¹ (as a fraction)? =
  7. 7.What is the value of 2¹ × 2⁻⁶? =
  8. 8.What is the value of 2²? =
  9. 9.Write 4.4 × 10⁻³ as a decimal. =
  10. 10.Write 4,90,00,000 in standard form as 4.9 × 10ⁿ. What is n?
  11. 11.Write (3⁸)⁹ as a single power 3ⁿ. What is n?
  12. 12.Write 4⁷ × 4³ as a single power 4ⁿ. What is n?
  13. 13.6.9 × 10⁴ =
  14. 14.What is the value of (3/8)⁻²? =
  15. 15.Write 4⁵ ÷ 4³ as a single power 4ⁿ. What is n?
  16. 16.What is the value of 7⁴? =
  17. 17.1.6 × 10⁴ =
  18. 18.What is the value of 2⁶? =
  19. 19.What is the value of 10² × 10⁻¹? =
  20. 20.What is the value of 5³ × 5⁻²? =
  21. 21.5 × 10² =
  22. 22.What is the value of (4/7)⁻¹? =
  23. 23.What is the value of (3/8)⁻¹? =
  24. 24.Write (8⁵)⁵ as a single power 8ⁿ. What is n?
  25. 25.Write 2¹³ ÷ 2⁵ as a single power 2ⁿ. What is n?
  26. 26.What is the value of 3² × 3⁻³? =
  27. 27.What is the value of 6⁵? =
  28. 28.What is the value of 5⁶ × 5⁻⁵? =
  29. 29.What is the value of 2³? =
  30. 30.Write 310 in standard form as 3.1 × 10ⁿ. What is n?
  31. 31.What is the value of 8³? =
  32. 32.What is the value of (1/4)⁻²? =
  33. 33.Write 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  34. 34.Write 1.6 × 10⁻² as a decimal. =
  35. 35.What is the value of 10³ × 10⁻⁶? =
  36. 36.What is the value of 6⁻³ (as a fraction)? =
  37. 37.What is the value of 10⁴? =
  38. 38.Write 31,000 in standard form as 3.1 × 10ⁿ. What is n?
  39. 39.Write 3.1 × 10⁻² as a decimal. =
  40. 40.Write (3³)² as a single power 3ⁿ. What is n?

Answer key

  1. 1/81
  2. 9/5
  3. 6561
  4. 9
  5. 2600000
  6. 1/7
  7. 1/32
  8. 4
  9. 0.0044
  10. 7
  11. 72
  12. 10
  13. 69000
  14. 64/9
  15. 2
  16. 2401
  17. 16000
  18. 64
  19. 10
  20. 5
  21. 500
  22. 7/4
  23. 8/3
  24. 25
  25. 8
  26. 1/3
  27. 7776
  28. 5
  29. 8
  30. 2
  31. 512
  32. 16
  33. 3
  34. 0.016
  35. 1/1000
  36. 1/216
  37. 10000
  38. 4
  39. 0.031
  40. 6

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