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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 872 · 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.Write 4⁶ × 4⁹ as a single power 4ⁿ. What is n?
  2. 2.Write 5⁵ × 5³ as a single power 5ⁿ. What is n?
  3. 3.What is the value of (3/4)⁻¹? =
  4. 4.What is the value of 3⁵ × 3⁻⁴? =
  5. 5.Write 4³ × 4⁵ as a single power 4ⁿ. What is n?
  6. 6.What is the value of 2⁶ × 2⁻³? =
  7. 7.What is the value of 8³? =
  8. 8.What is the value of 4⁻¹ (as a fraction)? =
  9. 9.What is the value of 2⁴ × 2⁻⁶? =
  10. 10.What is the value of (5/6)⁻²? =
  11. 11.Write 2.7 × 10⁻² as a decimal. =
  12. 12.Write 2⁹ ÷ 2⁶ as a single power 2ⁿ. What is n?
  13. 13.What is the value of 2¹⁶? =
  14. 14.What is the value of 2⁵ × 2⁻⁴? =
  15. 15.Write 9.1 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of (1/9)⁻²? =
  17. 17.What is the value of 3⁶ × 3⁻²? =
  18. 18.What is the value of 9³? =
  19. 19.Write 41,00,000 in standard form as 4.1 × 10ⁿ. What is n?
  20. 20.What is the value of 2⁻⁵ (as a fraction)? =
  21. 21.Write 6,900 in standard form as 6.9 × 10ⁿ. What is n?
  22. 22.7.5 × 10⁵ =
  23. 23.9.1 × 10⁶ =
  24. 24.2 × 10⁴ =
  25. 25.Write 4.2 × 10⁻² as a decimal. =
  26. 26.What is the value of (2/7)⁻¹? =
  27. 27.What is the value of 2⁶ × 2⁻⁵? =
  28. 28.Write 9,20,000 in standard form as 9.2 × 10ⁿ. What is n?
  29. 29.7.5 × 10² =
  30. 30.What is the value of 2⁻⁹ (as a fraction)? =
  31. 31.What is the value of 3⁶ × 3⁻⁴? =
  32. 32.What is the value of 7³? =
  33. 33.Write 9² × 9⁹ as a single power 9ⁿ. What is n?
  34. 34.What is the value of (5/6)⁻¹? =
  35. 35.What is the value of 2⁻⁷ (as a fraction)? =
  36. 36.What is the value of 10¹ × 10⁻²? =
  37. 37.What is the value of (5/8)⁻¹? =
  38. 38.Write (9²)⁸ as a single power 9ⁿ. What is n?
  39. 39.What is the value of 7⁻¹ (as a fraction)? =
  40. 40.4.2 × 10⁴ =

Answer key

  1. 15
  2. 8
  3. 4/3
  4. 3
  5. 8
  6. 8
  7. 512
  8. 1/4
  9. 1/4
  10. 36/25
  11. 0.027
  12. 3
  13. 65536
  14. 2
  15. 0.00091
  16. 81
  17. 81
  18. 729
  19. 6
  20. 1/32
  21. 3
  22. 750000
  23. 9100000
  24. 20000
  25. 0.042
  26. 7/2
  27. 2
  28. 5
  29. 750
  30. 1/512
  31. 9
  32. 343
  33. 11
  34. 6/5
  35. 1/128
  36. 1/10
  37. 8/5
  38. 16
  39. 1/7
  40. 42000

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