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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 158 · 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 2⁵ × 2⁻⁴? =
  2. 2.Write 4,500 in standard form as 4.5 × 10ⁿ. What is n?
  3. 3.1.2 × 10⁴ =
  4. 4.What is the value of 10⁵ × 10⁻³? =
  5. 5.What is the value of 3³? =
  6. 6.Write (2³)⁷ as a single power 2ⁿ. What is n?
  7. 7.Write 3.7 × 10⁻¹ as a decimal. =
  8. 8.Write 400 in standard form as 4 × 10ⁿ. What is n?
  9. 9.What is the value of 2⁵ × 2⁻⁶? =
  10. 10.6.1 × 10⁴ =
  11. 11.What is the value of 2⁶? =
  12. 12.What is the value of 6⁻¹ (as a fraction)? =
  13. 13.Write 4⁶ ÷ 4⁴ as a single power 4ⁿ. What is n?
  14. 14.Write 6⁹ ÷ 6⁶ as a single power 6ⁿ. What is n?
  15. 15.What is the value of 6³? =
  16. 16.Write 3⁶ × 3⁴ as a single power 3ⁿ. What is n?
  17. 17.What is the value of 3²? =
  18. 18.Write 6² × 6⁷ as a single power 6ⁿ. What is n?
  19. 19.Write 2.3 × 10⁻³ as a decimal. =
  20. 20.What is the value of (6/7)⁻²? =
  21. 21.6 × 10² =
  22. 22.6.9 × 10⁵ =
  23. 23.Write (3⁷)² as a single power 3ⁿ. What is n?
  24. 24.What is the value of 2¹⁵? =
  25. 25.What is the value of 10³ × 10⁻⁵? =
  26. 26.What is the value of 10³? =
  27. 27.What is the value of 7³? =
  28. 28.What is the value of 4⁻⁴ (as a fraction)? =
  29. 29.What is the value of 3⁻² (as a fraction)? =
  30. 30.What is the value of 2¹ × 2⁻¹? =
  31. 31.What is the value of (1/3)⁻¹? =
  32. 32.2.5 × 10⁴ =
  33. 33.Write (5²)⁷ as a single power 5ⁿ. What is n?
  34. 34.Write 2 × 10⁻³ as a decimal. =
  35. 35.What is the value of 2⁻¹ (as a fraction)? =
  36. 36.What is the value of 2⁷? =
  37. 37.What is the value of 10⁻³ (as a fraction)? =
  38. 38.What is the value of 3¹ × 3⁻¹? =
  39. 39.What is the value of 5⁴ × 5⁻³? =
  40. 40.Write 2 × 10⁻¹ as a decimal. =

Answer key

  1. 2
  2. 3
  3. 12000
  4. 100
  5. 27
  6. 21
  7. 0.37
  8. 2
  9. 1/2
  10. 61000
  11. 64
  12. 1/6
  13. 2
  14. 3
  15. 216
  16. 10
  17. 9
  18. 9
  19. 0.0023
  20. 49/36
  21. 600
  22. 690000
  23. 14
  24. 32768
  25. 1/100
  26. 1000
  27. 343
  28. 1/256
  29. 1/9
  30. 1
  31. 3
  32. 25000
  33. 14
  34. 0.002
  35. 1/2
  36. 128
  37. 1/1000
  38. 1
  39. 5
  40. 0.2

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