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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 686 · 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 5⁹ × 5⁷ as a single power 5ⁿ. What is n?
  2. 2.Write 2.5 × 10⁻³ as a decimal. =
  3. 3.What is the value of 5⁻⁴ (as a fraction)? =
  4. 4.What is the value of 4⁴? =
  5. 5.Write 11,000 in standard form as 1.1 × 10ⁿ. What is n?
  6. 6.What is the value of 5³? =
  7. 7.Write 1.1 × 10⁻¹ as a decimal. =
  8. 8.What is the value of 3¹ × 3⁻¹? =
  9. 9.What is the value of 5⁶ × 5⁻³? =
  10. 10.What is the value of 5⁶ × 5⁻²? =
  11. 11.What is the value of (4/7)⁻¹? =
  12. 12.What is the value of 2⁵ × 2⁻⁴? =
  13. 13.What is the value of 2⁶ × 2⁻⁵? =
  14. 14.Write (3⁸)⁸ as a single power 3ⁿ. What is n?
  15. 15.Write 1.6 × 10⁻⁴ as a decimal. =
  16. 16.Write 4.2 × 10⁻¹ as a decimal. =
  17. 17.2.2 × 10² =
  18. 18.What is the value of 3⁻¹ (as a fraction)? =
  19. 19.What is the value of 6³? =
  20. 20.What is the value of 3⁵ × 3⁻⁵? =
  21. 21.What is the value of 5³ × 5⁻⁴? =
  22. 22.What is the value of 4⁵? =
  23. 23.Write 3³ × 3⁴ as a single power 3ⁿ. What is n?
  24. 24.What is the value of 8³? =
  25. 25.What is the value of 9⁻³ (as a fraction)? =
  26. 26.Write 2⁹ ÷ 2² as a single power 2ⁿ. What is n?
  27. 27.What is the value of 5⁵ × 5⁻²? =
  28. 28.What is the value of 4³? =
  29. 29.Write (9³)⁹ as a single power 9ⁿ. What is n?
  30. 30.Write 4,50,00,000 in standard form as 4.5 × 10ⁿ. What is n?
  31. 31.What is the value of (8/9)⁻¹? =
  32. 32.Write 7⁸ ÷ 7² as a single power 7ⁿ. What is n?
  33. 33.What is the value of 2³? =
  34. 34.What is the value of 2² × 2⁻¹? =
  35. 35.Write 7.7 × 10⁻⁴ as a decimal. =
  36. 36.What is the value of 5⁴ × 5⁻²? =
  37. 37.What is the value of 3² × 3⁻³? =
  38. 38.Write 5¹² ÷ 5⁹ as a single power 5ⁿ. What is n?
  39. 39.Write 93,00,000 in standard form as 9.3 × 10ⁿ. What is n?
  40. 40.Write 2⁷ ÷ 2⁴ as a single power 2ⁿ. What is n?

Answer key

  1. 16
  2. 0.0025
  3. 1/625
  4. 256
  5. 4
  6. 125
  7. 0.11
  8. 1
  9. 125
  10. 625
  11. 7/4
  12. 2
  13. 2
  14. 64
  15. 0.00016
  16. 0.42
  17. 220
  18. 1/3
  19. 216
  20. 1
  21. 1/5
  22. 1024
  23. 7
  24. 512
  25. 1/729
  26. 7
  27. 125
  28. 64
  29. 27
  30. 7
  31. 9/8
  32. 6
  33. 8
  34. 2
  35. 0.00077
  36. 25
  37. 1/3
  38. 3
  39. 6
  40. 3

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