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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 163 · 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 3¹ × 3⁻¹? =
  2. 2.What is the value of 3⁵ × 3⁻³? =
  3. 3.Write 4.2 × 10⁻³ as a decimal. =
  4. 4.Write 62,000 in standard form as 6.2 × 10ⁿ. What is n?
  5. 5.Write 4⁶ × 4⁶ as a single power 4ⁿ. What is n?
  6. 6.What is the value of 10⁻¹ (as a fraction)? =
  7. 7.What is the value of 6⁴? =
  8. 8.Write 6⁸ ÷ 6⁶ as a single power 6ⁿ. What is n?
  9. 9.Write 5 × 10⁻² as a decimal. =
  10. 10.What is the value of 5³ × 5⁻⁴? =
  11. 11.What is the value of 3² × 3⁻⁴? =
  12. 12.Write 2,50,00,000 in standard form as 2.5 × 10ⁿ. What is n?
  13. 13.What is the value of 3¹ × 3⁻⁴? =
  14. 14.Write 6¹² ÷ 6⁸ as a single power 6ⁿ. What is n?
  15. 15.Write 5,400 in standard form as 5.4 × 10ⁿ. What is n?
  16. 16.Write 2⁷ × 2⁵ as a single power 2ⁿ. What is n?
  17. 17.What is the value of 2⁵ × 2⁻³? =
  18. 18.What is the value of 2⁹? =
  19. 19.5.3 × 10⁵ =
  20. 20.Write 7.8 × 10⁻³ as a decimal. =
  21. 21.6.2 × 10³ =
  22. 22.What is the value of 10⁴ × 10⁻⁶? =
  23. 23.What is the value of 3⁻⁵ (as a fraction)? =
  24. 24.Write 8.6 × 10⁻² as a decimal. =
  25. 25.What is the value of (1/4)⁻²? =
  26. 26.Write 1.6 × 10⁻² as a decimal. =
  27. 27.Write 8,000 in standard form as 8 × 10ⁿ. What is n?
  28. 28.8.6 × 10⁴ =
  29. 29.Write 6.7 × 10⁻³ as a decimal. =
  30. 30.Write 3⁷ × 3⁸ as a single power 3ⁿ. What is n?
  31. 31.Write 3.6 × 10⁻² as a decimal. =
  32. 32.Write 65,000 in standard form as 6.5 × 10ⁿ. What is n?
  33. 33.What is the value of 5¹ × 5⁻¹? =
  34. 34.Write 790 in standard form as 7.9 × 10ⁿ. What is n?
  35. 35.What is the value of 5⁴ × 5⁻⁴? =
  36. 36.Write (4⁸)³ as a single power 4ⁿ. What is n?
  37. 37.What is the value of 7⁻¹ (as a fraction)? =
  38. 38.Write 2⁴ × 2⁸ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 3⁹? =
  40. 40.Write 7⁷ × 7⁶ as a single power 7ⁿ. What is n?

Answer key

  1. 1
  2. 9
  3. 0.0042
  4. 4
  5. 12
  6. 1/10
  7. 1296
  8. 2
  9. 0.05
  10. 1/5
  11. 1/9
  12. 7
  13. 1/27
  14. 4
  15. 3
  16. 12
  17. 4
  18. 512
  19. 530000
  20. 0.0078
  21. 6200
  22. 1/100
  23. 1/243
  24. 0.086
  25. 16
  26. 0.016
  27. 3
  28. 86000
  29. 0.0067
  30. 15
  31. 0.036
  32. 4
  33. 1
  34. 2
  35. 1
  36. 24
  37. 1/7
  38. 12
  39. 19683
  40. 13

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