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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 774 · 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 5¹ × 5⁻²? =
  2. 2.7.7 × 10⁵ =
  3. 3.What is the value of (5/9)⁻¹? =
  4. 4.Write (2²)² as a single power 2ⁿ. What is n?
  5. 5.What is the value of 4⁻⁴ (as a fraction)? =
  6. 6.What is the value of 3² × 3⁻²? =
  7. 7.Write 4.2 × 10⁻⁴ as a decimal. =
  8. 8.What is the value of 3⁵ × 3⁻²? =
  9. 9.What is the value of 4⁸? =
  10. 10.What is the value of (1/8)⁻¹? =
  11. 11.What is the value of 5⁶? =
  12. 12.What is the value of 2¹⁴? =
  13. 13.1.7 × 10² =
  14. 14.What is the value of 8⁴? =
  15. 15.Write (5⁴)⁹ as a single power 5ⁿ. What is n?
  16. 16.Write 8¹⁴ ÷ 8⁵ as a single power 8ⁿ. What is n?
  17. 17.Write (3⁶)⁸ as a single power 3ⁿ. What is n?
  18. 18.What is the value of (2/7)⁻¹? =
  19. 19.Write 4² × 4³ as a single power 4ⁿ. What is n?
  20. 20.What is the value of 10² × 10⁻⁵? =
  21. 21.Write 3¹⁴ ÷ 3⁹ as a single power 3ⁿ. What is n?
  22. 22.Write 4¹⁰ ÷ 4⁶ as a single power 4ⁿ. What is n?
  23. 23.Write 82,00,000 in standard form as 8.2 × 10ⁿ. What is n?
  24. 24.Write 20,00,000 in standard form as 2 × 10ⁿ. What is n?
  25. 25.What is the value of 5¹ × 5⁻³? =
  26. 26.Write 2,80,000 in standard form as 2.8 × 10ⁿ. What is n?
  27. 27.What is the value of 3⁻¹ (as a fraction)? =
  28. 28.What is the value of 5¹ × 5⁻¹? =
  29. 29.3.2 × 10⁷ =
  30. 30.Write 3 × 10⁻³ as a decimal. =
  31. 31.What is the value of 4⁷? =
  32. 32.8.7 × 10⁴ =
  33. 33.Write 1.5 × 10⁻² as a decimal. =
  34. 34.What is the value of (3/5)⁻¹? =
  35. 35.Write 5³ × 5⁴ as a single power 5ⁿ. What is n?
  36. 36.What is the value of 3¹⁰? =
  37. 37.What is the value of 3³ × 3⁻²? =
  38. 38.Write 8.3 × 10⁻¹ as a decimal. =
  39. 39.What is the value of 10³? =
  40. 40.Write 59,00,000 in standard form as 5.9 × 10ⁿ. What is n?

Answer key

  1. 1/5
  2. 770000
  3. 9/5
  4. 4
  5. 1/256
  6. 1
  7. 0.00042
  8. 27
  9. 65536
  10. 8
  11. 15625
  12. 16384
  13. 170
  14. 4096
  15. 36
  16. 9
  17. 48
  18. 7/2
  19. 5
  20. 1/1000
  21. 5
  22. 4
  23. 6
  24. 6
  25. 1/25
  26. 5
  27. 1/3
  28. 1
  29. 32000000
  30. 0.003
  31. 16384
  32. 87000
  33. 0.015
  34. 5/3
  35. 7
  36. 59049
  37. 3
  38. 0.83
  39. 1000
  40. 6

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