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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 857 · 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 2¹⁵? =
  2. 2.What is the value of (5/8)⁻¹? =
  3. 3.Write 20,00,000 in standard form as 2 × 10ⁿ. What is n?
  4. 4.Write 2,700 in standard form as 2.7 × 10ⁿ. What is n?
  5. 5.What is the value of 3⁻¹ (as a fraction)? =
  6. 6.What is the value of 5⁴ × 5⁻³? =
  7. 7.What is the value of 5³ × 5⁻⁵? =
  8. 8.What is the value of 2¹¹? =
  9. 9.2.5 × 10³ =
  10. 10.What is the value of 10¹ × 10⁻²? =
  11. 11.What is the value of (4/9)⁻¹? =
  12. 12.Write 16,00,000 in standard form as 1.6 × 10ⁿ. What is n?
  13. 13.What is the value of 4³? =
  14. 14.Write 3⁴ ÷ 3² as a single power 3ⁿ. What is n?
  15. 15.What is the value of 4⁴? =
  16. 16.What is the value of 10² × 10⁻²? =
  17. 17.What is the value of 3¹⁰? =
  18. 18.Write 7,60,00,000 in standard form as 7.6 × 10ⁿ. What is n?
  19. 19.Write 3 × 10⁻⁴ as a decimal. =
  20. 20.Write 6⁶ × 6² as a single power 6ⁿ. What is n?
  21. 21.What is the value of 3⁶ × 3⁻⁶? =
  22. 22.What is the value of 6⁻¹ (as a fraction)? =
  23. 23.What is the value of 3¹ × 3⁻²? =
  24. 24.Write 8³ × 8⁷ as a single power 8ⁿ. What is n?
  25. 25.Write 9.4 × 10⁻² as a decimal. =
  26. 26.Write 7.5 × 10⁻³ as a decimal. =
  27. 27.Write (7²)³ as a single power 7ⁿ. What is n?
  28. 28.What is the value of 2¹⁶? =
  29. 29.Write 340 in standard form as 3.4 × 10ⁿ. What is n?
  30. 30.Write 8¹⁶ ÷ 8⁸ as a single power 8ⁿ. What is n?
  31. 31.Write 3.2 × 10⁻³ as a decimal. =
  32. 32.Write 8⁹ × 8⁸ as a single power 8ⁿ. What is n?
  33. 33.Write 2¹¹ ÷ 2⁷ as a single power 2ⁿ. What is n?
  34. 34.What is the value of 3⁵ × 3⁻⁵? =
  35. 35.What is the value of 10³ × 10⁻⁵? =
  36. 36.What is the value of (1/6)⁻²? =
  37. 37.What is the value of 2⁶ × 2⁻⁴? =
  38. 38.Write 3⁶ × 3² as a single power 3ⁿ. What is n?
  39. 39.What is the value of (3/7)⁻²? =
  40. 40.What is the value of 2⁵ × 2⁻¹? =

Answer key

  1. 32768
  2. 8/5
  3. 6
  4. 3
  5. 1/3
  6. 5
  7. 1/25
  8. 2048
  9. 2500
  10. 1/10
  11. 9/4
  12. 6
  13. 64
  14. 2
  15. 256
  16. 1
  17. 59049
  18. 7
  19. 0.0003
  20. 8
  21. 1
  22. 1/6
  23. 1/3
  24. 10
  25. 0.094
  26. 0.0075
  27. 6
  28. 65536
  29. 2
  30. 8
  31. 0.0032
  32. 17
  33. 4
  34. 1
  35. 1/100
  36. 36
  37. 4
  38. 8
  39. 49/9
  40. 16

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