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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 366 · 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 5³ × 5⁻¹? =
  2. 2.4.6 × 10⁵ =
  3. 3.Write 1,400 in standard form as 1.4 × 10ⁿ. What is n?
  4. 4.Write 9.6 × 10⁻² as a decimal. =
  5. 5.Write 4.2 × 10⁻⁴ as a decimal. =
  6. 6.Write 2.9 × 10⁻³ as a decimal. =
  7. 7.Write (7⁸)⁶ as a single power 7ⁿ. What is n?
  8. 8.Write 3³ × 3³ as a single power 3ⁿ. What is n?
  9. 9.1.6 × 10⁴ =
  10. 10.Write (5⁴)⁸ as a single power 5ⁿ. What is n?
  11. 11.What is the value of 4²? =
  12. 12.Write 7.8 × 10⁻¹ as a decimal. =
  13. 13.What is the value of 2⁻⁵ (as a fraction)? =
  14. 14.Write 8.2 × 10⁻² as a decimal. =
  15. 15.What is the value of 8⁴? =
  16. 16.What is the value of 8⁵? =
  17. 17.What is the value of (5/9)⁻¹? =
  18. 18.What is the value of 8⁻² (as a fraction)? =
  19. 19.Write (8⁷)² as a single power 8ⁿ. What is n?
  20. 20.What is the value of 2¹ × 2⁻⁴? =
  21. 21.Write 4.6 × 10⁻¹ as a decimal. =
  22. 22.What is the value of (3/7)⁻¹? =
  23. 23.What is the value of 7²? =
  24. 24.What is the value of (5/6)⁻²? =
  25. 25.1.5 × 10⁶ =
  26. 26.What is the value of 7⁻² (as a fraction)? =
  27. 27.3 × 10² =
  28. 28.9.9 × 10² =
  29. 29.6.7 × 10⁵ =
  30. 30.Write 46,000 in standard form as 4.6 × 10ⁿ. What is n?
  31. 31.What is the value of 4³? =
  32. 32.Write 7⁵ × 7⁷ as a single power 7ⁿ. What is n?
  33. 33.Write 5,400 in standard form as 5.4 × 10ⁿ. What is n?
  34. 34.What is the value of 3⁵? =
  35. 35.Write 2⁴ × 2⁹ as a single power 2ⁿ. What is n?
  36. 36.What is the value of 2² × 2⁻⁵? =
  37. 37.Write 5.2 × 10⁻² as a decimal. =
  38. 38.Write (7⁸)⁹ as a single power 7ⁿ. What is n?
  39. 39.What is the value of 2³ × 2⁻¹? =
  40. 40.What is the value of 10⁴ × 10⁻³? =

Answer key

  1. 25
  2. 460000
  3. 3
  4. 0.096
  5. 0.00042
  6. 0.0029
  7. 48
  8. 6
  9. 16000
  10. 32
  11. 16
  12. 0.78
  13. 1/32
  14. 0.082
  15. 4096
  16. 32768
  17. 9/5
  18. 1/64
  19. 14
  20. 1/8
  21. 0.46
  22. 7/3
  23. 49
  24. 36/25
  25. 1500000
  26. 1/49
  27. 300
  28. 990
  29. 670000
  30. 4
  31. 64
  32. 12
  33. 3
  34. 243
  35. 13
  36. 1/8
  37. 0.052
  38. 72
  39. 4
  40. 10

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