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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 810 · 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 3³ × 3⁻³? =
  2. 2.9.1 × 10³ =
  3. 3.Write 9⁸ ÷ 9³ as a single power 9ⁿ. What is n?
  4. 4.What is the value of 2¹ × 2⁻⁵? =
  5. 5.Write (7⁹)⁷ as a single power 7ⁿ. What is n?
  6. 6.Write 3,40,000 in standard form as 3.4 × 10ⁿ. What is n?
  7. 7.What is the value of 2⁹? =
  8. 8.Write 7.6 × 10⁻² as a decimal. =
  9. 9.What is the value of (1/5)⁻²? =
  10. 10.Write 9³ × 9⁴ as a single power 9ⁿ. What is n?
  11. 11.What is the value of (3/5)⁻²? =
  12. 12.Write 2 × 10⁻³ as a decimal. =
  13. 13.What is the value of 4⁷? =
  14. 14.Write 9⁸ × 9⁷ as a single power 9ⁿ. What is n?
  15. 15.What is the value of 2² × 2⁻¹? =
  16. 16.5.2 × 10² =
  17. 17.Write 1.3 × 10⁻⁴ as a decimal. =
  18. 18.8.8 × 10⁷ =
  19. 19.Write 1,40,000 in standard form as 1.4 × 10ⁿ. What is n?
  20. 20.What is the value of 10³ × 10⁻¹? =
  21. 21.What is the value of 10¹ × 10⁻⁴? =
  22. 22.Write 8¹³ ÷ 8⁴ as a single power 8ⁿ. What is n?
  23. 23.Write 4⁸ × 4² as a single power 4ⁿ. What is n?
  24. 24.What is the value of 9²? =
  25. 25.Write 2.9 × 10⁻¹ as a decimal. =
  26. 26.What is the value of (3/8)⁻²? =
  27. 27.What is the value of 10¹ × 10⁻⁶? =
  28. 28.Write 8.1 × 10⁻¹ as a decimal. =
  29. 29.2.2 × 10⁷ =
  30. 30.What is the value of 3⁵ × 3⁻⁵? =
  31. 31.What is the value of 7³? =
  32. 32.What is the value of 2⁻⁷ (as a fraction)? =
  33. 33.What is the value of 2¹⁵? =
  34. 34.What is the value of 6⁻² (as a fraction)? =
  35. 35.Write 5.1 × 10⁻³ as a decimal. =
  36. 36.What is the value of 2¹ × 2⁻²? =
  37. 37.Write 2⁴ × 2⁵ as a single power 2ⁿ. What is n?
  38. 38.What is the value of 3³ × 3⁻⁶? =
  39. 39.Write 52,000 in standard form as 5.2 × 10ⁿ. What is n?
  40. 40.What is the value of 5⁻² (as a fraction)? =

Answer key

  1. 1
  2. 9100
  3. 5
  4. 1/16
  5. 63
  6. 5
  7. 512
  8. 0.076
  9. 25
  10. 7
  11. 25/9
  12. 0.002
  13. 16384
  14. 15
  15. 2
  16. 520
  17. 0.00013
  18. 88000000
  19. 5
  20. 100
  21. 1/1000
  22. 9
  23. 10
  24. 81
  25. 0.29
  26. 64/9
  27. 1/100000
  28. 0.81
  29. 22000000
  30. 1
  31. 343
  32. 1/128
  33. 32768
  34. 1/36
  35. 0.0051
  36. 1/2
  37. 9
  38. 1/27
  39. 4
  40. 1/25

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