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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 543 · 40 sums
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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 2⁻¹ (as a fraction)? =
  2. 2.What is the value of 3¹ × 3⁻²? =
  3. 3.What is the value of 2¹ × 2⁻¹? =
  4. 4.What is the value of 10¹ × 10⁻⁵? =
  5. 5.What is the value of 2⁹? =
  6. 6.Write (6³)⁴ as a single power 6ⁿ. What is n?
  7. 7.Write 8⁴ × 8⁹ as a single power 8ⁿ. What is n?
  8. 8.Write (3⁴)⁴ as a single power 3ⁿ. What is n?
  9. 9.What is the value of 2¹²? =
  10. 10.Write (3³)² as a single power 3ⁿ. What is n?
  11. 11.Write 6.5 × 10⁻¹ as a decimal. =
  12. 12.Write 2.5 × 10⁻¹ as a decimal. =
  13. 13.Write 720 in standard form as 7.2 × 10ⁿ. What is n?
  14. 14.Write 9⁸ × 9⁶ as a single power 9ⁿ. What is n?
  15. 15.What is the value of 2⁷? =
  16. 16.What is the value of (3/8)⁻²? =
  17. 17.Write 9 × 10⁻⁴ as a decimal. =
  18. 18.What is the value of 5⁴ × 5⁻²? =
  19. 19.Write 8⁷ × 8⁵ as a single power 8ⁿ. What is n?
  20. 20.What is the value of (1/6)⁻¹? =
  21. 21.7.4 × 10⁷ =
  22. 22.What is the value of (1/3)⁻²? =
  23. 23.Write 1.4 × 10⁻¹ as a decimal. =
  24. 24.2.6 × 10⁵ =
  25. 25.What is the value of 2¹⁴? =
  26. 26.What is the value of 2⁴? =
  27. 27.What is the value of 3³ × 3⁻²? =
  28. 28.What is the value of 5⁶? =
  29. 29.Write 750 in standard form as 7.5 × 10ⁿ. What is n?
  30. 30.Write 4,00,00,000 in standard form as 4 × 10ⁿ. What is n?
  31. 31.Write (4⁵)³ as a single power 4ⁿ. What is n?
  32. 32.Write (4²)⁹ as a single power 4ⁿ. What is n?
  33. 33.Write 5,100 in standard form as 5.1 × 10ⁿ. What is n?
  34. 34.What is the value of 10⁴? =
  35. 35.Write 95,00,000 in standard form as 9.5 × 10ⁿ. What is n?
  36. 36.Write 4.1 × 10⁻² as a decimal. =
  37. 37.Write 2¹⁰ ÷ 2² as a single power 2ⁿ. What is n?
  38. 38.2.3 × 10² =
  39. 39.Write 4² × 4⁴ as a single power 4ⁿ. What is n?
  40. 40.What is the value of 3⁵ × 3⁻²? =

Answer key

  1. 1/2
  2. 1/3
  3. 1
  4. 1/10000
  5. 512
  6. 12
  7. 13
  8. 16
  9. 4096
  10. 6
  11. 0.65
  12. 0.25
  13. 2
  14. 14
  15. 128
  16. 64/9
  17. 0.0009
  18. 25
  19. 12
  20. 6
  21. 74000000
  22. 9
  23. 0.14
  24. 260000
  25. 16384
  26. 16
  27. 3
  28. 15625
  29. 2
  30. 7
  31. 15
  32. 18
  33. 3
  34. 10000
  35. 6
  36. 0.041
  37. 8
  38. 230
  39. 6
  40. 27

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