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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 140 · 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 8⁻³ (as a fraction)? =
  2. 2.Write 770 in standard form as 7.7 × 10ⁿ. What is n?
  3. 3.What is the value of (1/7)⁻¹? =
  4. 4.What is the value of 2⁶ × 2⁻⁶? =
  5. 5.Write 1.6 × 10⁻⁴ as a decimal. =
  6. 6.What is the value of 5³? =
  7. 7.Write 2¹³ ÷ 2⁴ as a single power 2ⁿ. What is n?
  8. 8.What is the value of (4/9)⁻¹? =
  9. 9.What is the value of (4/9)⁻²? =
  10. 10.Write 4³ × 4⁵ as a single power 4ⁿ. What is n?
  11. 11.What is the value of 9⁴? =
  12. 12.Write 5¹⁸ ÷ 5⁹ as a single power 5ⁿ. What is n?
  13. 13.Write 45,000 in standard form as 4.5 × 10ⁿ. What is n?
  14. 14.What is the value of 5⁴? =
  15. 15.What is the value of 9⁻¹ (as a fraction)? =
  16. 16.What is the value of 10² × 10⁻¹? =
  17. 17.What is the value of (2/3)⁻²? =
  18. 18.Write 7,10,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  19. 19.What is the value of 3⁶ × 3⁻⁴? =
  20. 20.3.8 × 10³ =
  21. 21.Write 48,00,000 in standard form as 4.8 × 10ⁿ. What is n?
  22. 22.Write 8¹⁶ ÷ 8⁹ as a single power 8ⁿ. What is n?
  23. 23.Write 1.8 × 10⁻⁴ as a decimal. =
  24. 24.What is the value of 5² × 5⁻⁴? =
  25. 25.What is the value of 4⁻² (as a fraction)? =
  26. 26.What is the value of 5⁴ × 5⁻⁵? =
  27. 27.Write 4.2 × 10⁻¹ as a decimal. =
  28. 28.What is the value of 2² × 2⁻¹? =
  29. 29.What is the value of 8⁴? =
  30. 30.What is the value of (5/6)⁻¹? =
  31. 31.2.7 × 10² =
  32. 32.Write 9¹¹ ÷ 9³ as a single power 9ⁿ. What is n?
  33. 33.What is the value of 2² × 2⁻³? =
  34. 34.Write 3¹⁴ ÷ 3⁵ as a single power 3ⁿ. What is n?
  35. 35.What is the value of 2¹ × 2⁻⁴? =
  36. 36.Write (2²)³ as a single power 2ⁿ. What is n?
  37. 37.What is the value of 9⁻² (as a fraction)? =
  38. 38.What is the value of 10⁻¹ (as a fraction)? =
  39. 39.What is the value of 10³ × 10⁻⁴? =
  40. 40.What is the value of 2⁵? =

Answer key

  1. 1/512
  2. 2
  3. 7
  4. 1
  5. 0.00016
  6. 125
  7. 9
  8. 9/4
  9. 81/16
  10. 8
  11. 6561
  12. 9
  13. 4
  14. 625
  15. 1/9
  16. 10
  17. 9/4
  18. 7
  19. 9
  20. 3800
  21. 6
  22. 7
  23. 0.00018
  24. 1/25
  25. 1/16
  26. 1/5
  27. 0.42
  28. 2
  29. 4096
  30. 6/5
  31. 270
  32. 8
  33. 1/2
  34. 9
  35. 1/8
  36. 6
  37. 1/81
  38. 1/10
  39. 1/10
  40. 32

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