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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 545 · 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 3⁵ × 3⁶ as a single power 3ⁿ. What is n?
  2. 2.What is the value of 10⁴ × 10⁻³? =
  3. 3.Write 4,900 in standard form as 4.9 × 10ⁿ. What is n?
  4. 4.What is the value of (7/9)⁻²? =
  5. 5.What is the value of 5³ × 5⁻⁵? =
  6. 6.What is the value of 2⁸? =
  7. 7.What is the value of (1/5)⁻²? =
  8. 8.What is the value of 5²? =
  9. 9.Write 3.5 × 10⁻² as a decimal. =
  10. 10.Write 63,00,000 in standard form as 6.3 × 10ⁿ. What is n?
  11. 11.Write 4⁹ × 4⁷ as a single power 4ⁿ. What is n?
  12. 12.Write 4⁹ ÷ 4⁴ as a single power 4ⁿ. What is n?
  13. 13.What is the value of (3/8)⁻¹? =
  14. 14.Write 9.8 × 10⁻² as a decimal. =
  15. 15.What is the value of 2³? =
  16. 16.What is the value of 5¹ × 5⁻³? =
  17. 17.What is the value of 3⁵? =
  18. 18.Write 7,000 in standard form as 7 × 10ⁿ. What is n?
  19. 19.What is the value of 3²? =
  20. 20.Write (4⁴)² as a single power 4ⁿ. What is n?
  21. 21.What is the value of 7⁵? =
  22. 22.What is the value of 3⁻⁵ (as a fraction)? =
  23. 23.What is the value of 8⁻³ (as a fraction)? =
  24. 24.What is the value of 5⁷? =
  25. 25.What is the value of 5³? =
  26. 26.What is the value of 2³ × 2⁻³? =
  27. 27.3 × 10³ =
  28. 28.What is the value of 3⁶ × 3⁻¹? =
  29. 29.What is the value of 3³? =
  30. 30.What is the value of 2⁴ × 2⁻¹? =
  31. 31.Write 6,90,00,000 in standard form as 6.9 × 10ⁿ. What is n?
  32. 32.What is the value of (5/7)⁻¹? =
  33. 33.Write 60,00,000 in standard form as 6 × 10ⁿ. What is n?
  34. 34.What is the value of 2¹ × 2⁻⁶? =
  35. 35.What is the value of (1/4)⁻²? =
  36. 36.What is the value of 10¹ × 10⁻⁶? =
  37. 37.What is the value of 2⁵ × 2⁻⁶? =
  38. 38.What is the value of 6³? =
  39. 39.Write 4⁵ × 4⁶ as a single power 4ⁿ. What is n?
  40. 40.What is the value of 6²? =

Answer key

  1. 11
  2. 10
  3. 3
  4. 81/49
  5. 1/25
  6. 256
  7. 25
  8. 25
  9. 0.035
  10. 6
  11. 16
  12. 5
  13. 8/3
  14. 0.098
  15. 8
  16. 1/25
  17. 243
  18. 3
  19. 9
  20. 8
  21. 16807
  22. 1/243
  23. 1/512
  24. 78125
  25. 125
  26. 1
  27. 3000
  28. 243
  29. 27
  30. 8
  31. 7
  32. 7/5
  33. 6
  34. 1/32
  35. 16
  36. 1/100000
  37. 1/2
  38. 216
  39. 11
  40. 36

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