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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 685 · 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 2⁻⁹ (as a fraction)? =
  2. 2.What is the value of 9⁻³ (as a fraction)? =
  3. 3.Write (2⁸)⁸ as a single power 2ⁿ. What is n?
  4. 4.1.8 × 10⁷ =
  5. 5.Write 9¹⁷ ÷ 9⁸ as a single power 9ⁿ. What is n?
  6. 6.Write (8²)⁶ as a single power 8ⁿ. What is n?
  7. 7.3 × 10⁵ =
  8. 8.What is the value of 3⁶? =
  9. 9.What is the value of 2² × 2⁻²? =
  10. 10.What is the value of 2⁶? =
  11. 11.What is the value of 6³? =
  12. 12.Write 3⁷ × 3³ as a single power 3ⁿ. What is n?
  13. 13.What is the value of 4⁻³ (as a fraction)? =
  14. 14.Write 8⁹ × 8⁸ as a single power 8ⁿ. What is n?
  15. 15.Write 4⁸ × 4³ as a single power 4ⁿ. What is n?
  16. 16.What is the value of 10⁻¹ (as a fraction)? =
  17. 17.What is the value of 2¹¹? =
  18. 18.Write 7⁷ × 7⁸ as a single power 7ⁿ. What is n?
  19. 19.8.1 × 10⁴ =
  20. 20.What is the value of 7⁵? =
  21. 21.Write 3⁸ ÷ 3³ as a single power 3ⁿ. What is n?
  22. 22.Write 1,10,000 in standard form as 1.1 × 10ⁿ. What is n?
  23. 23.What is the value of 2² × 2⁻⁴? =
  24. 24.What is the value of 7⁻¹ (as a fraction)? =
  25. 25.Write (4⁹)³ as a single power 4ⁿ. What is n?
  26. 26.Write 3¹⁰ ÷ 3³ as a single power 3ⁿ. What is n?
  27. 27.What is the value of 6⁴? =
  28. 28.Write 910 in standard form as 9.1 × 10ⁿ. What is n?
  29. 29.What is the value of 2¹²? =
  30. 30.Write 84,00,000 in standard form as 8.4 × 10ⁿ. What is n?
  31. 31.What is the value of (1/8)⁻²? =
  32. 32.What is the value of 3¹ × 3⁻²? =
  33. 33.What is the value of 2¹⁶? =
  34. 34.What is the value of 5² × 5⁻⁴? =
  35. 35.What is the value of (1/6)⁻²? =
  36. 36.What is the value of 3² × 3⁻⁵? =
  37. 37.Write 6.7 × 10⁻² as a decimal. =
  38. 38.What is the value of 5⁻³ (as a fraction)? =
  39. 39.5.2 × 10⁴ =
  40. 40.Write 52,000 in standard form as 5.2 × 10ⁿ. What is n?

Answer key

  1. 1/512
  2. 1/729
  3. 64
  4. 18000000
  5. 9
  6. 12
  7. 300000
  8. 729
  9. 1
  10. 64
  11. 216
  12. 10
  13. 1/64
  14. 17
  15. 11
  16. 1/10
  17. 2048
  18. 15
  19. 81000
  20. 16807
  21. 5
  22. 5
  23. 1/4
  24. 1/7
  25. 27
  26. 7
  27. 1296
  28. 2
  29. 4096
  30. 6
  31. 64
  32. 1/3
  33. 65536
  34. 1/25
  35. 36
  36. 1/27
  37. 0.067
  38. 1/125
  39. 52000
  40. 4

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