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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 407 · 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 1.2 × 10⁻¹ as a decimal. =
  2. 2.What is the value of 6⁻¹ (as a fraction)? =
  3. 3.What is the value of 3³? =
  4. 4.What is the value of (3/8)⁻²? =
  5. 5.What is the value of 10¹ × 10⁻³? =
  6. 6.Write 5,900 in standard form as 5.9 × 10ⁿ. What is n?
  7. 7.Write 5,20,000 in standard form as 5.2 × 10ⁿ. What is n?
  8. 8.Write (7⁶)³ as a single power 7ⁿ. What is n?
  9. 9.Write 6 × 10⁻⁴ as a decimal. =
  10. 10.What is the value of (3/7)⁻¹? =
  11. 11.What is the value of 4⁻⁴ (as a fraction)? =
  12. 12.2.9 × 10³ =
  13. 13.What is the value of 9⁻¹ (as a fraction)? =
  14. 14.What is the value of 5⁵ × 5⁻¹? =
  15. 15.7.4 × 10⁴ =
  16. 16.Write 5¹⁰ ÷ 5⁷ as a single power 5ⁿ. What is n?
  17. 17.Write 3⁶ × 3⁴ as a single power 3ⁿ. What is n?
  18. 18.What is the value of 2² × 2⁻⁵? =
  19. 19.Write 2.9 × 10⁻² as a decimal. =
  20. 20.1.8 × 10⁴ =
  21. 21.What is the value of 5⁴ × 5⁻⁶? =
  22. 22.What is the value of 2⁴ × 2⁻⁵? =
  23. 23.5.2 × 10³ =
  24. 24.1.7 × 10⁵ =
  25. 25.Write 91,00,000 in standard form as 9.1 × 10ⁿ. What is n?
  26. 26.Write 8¹² ÷ 8⁴ as a single power 8ⁿ. What is n?
  27. 27.What is the value of 4⁴? =
  28. 28.What is the value of 2⁶ × 2⁻⁵? =
  29. 29.What is the value of 2²? =
  30. 30.What is the value of 3³ × 3⁻¹? =
  31. 31.What is the value of (1/4)⁻²? =
  32. 32.Write 6⁹ × 6² as a single power 6ⁿ. What is n?
  33. 33.Write 7⁹ × 7⁷ as a single power 7ⁿ. What is n?
  34. 34.Write 3.2 × 10⁻⁴ as a decimal. =
  35. 35.Write (4³)⁹ as a single power 4ⁿ. What is n?
  36. 36.4.1 × 10² =
  37. 37.Write 2.5 × 10⁻³ as a decimal. =
  38. 38.What is the value of 7⁻¹ (as a fraction)? =
  39. 39.6.6 × 10⁵ =
  40. 40.What is the value of 8⁻¹ (as a fraction)? =

Answer key

  1. 0.12
  2. 1/6
  3. 27
  4. 64/9
  5. 1/100
  6. 3
  7. 5
  8. 18
  9. 0.0006
  10. 7/3
  11. 1/256
  12. 2900
  13. 1/9
  14. 625
  15. 74000
  16. 3
  17. 10
  18. 1/8
  19. 0.029
  20. 18000
  21. 1/25
  22. 1/2
  23. 5200
  24. 170000
  25. 6
  26. 8
  27. 256
  28. 2
  29. 4
  30. 9
  31. 16
  32. 11
  33. 16
  34. 0.00032
  35. 27
  36. 410
  37. 0.0025
  38. 1/7
  39. 660000
  40. 1/8

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