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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 345 · 40 sums
TalentJR

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 4⁵ × 4⁸ as a single power 4ⁿ. What is n?
  2. 2.What is the value of 9²? =
  3. 3.Write 8.3 × 10⁻¹ as a decimal. =
  4. 4.Write 1.8 × 10⁻¹ as a decimal. =
  5. 5.Write (7⁷)⁶ as a single power 7ⁿ. What is n?
  6. 6.Write 3⁶ × 3⁷ as a single power 3ⁿ. What is n?
  7. 7.Write 4,200 in standard form as 4.2 × 10ⁿ. What is n?
  8. 8.What is the value of 9⁴? =
  9. 9.Write 5,600 in standard form as 5.6 × 10ⁿ. What is n?
  10. 10.What is the value of (1/2)⁻²? =
  11. 11.What is the value of 3⁻² (as a fraction)? =
  12. 12.What is the value of 8³? =
  13. 13.Write 610 in standard form as 6.1 × 10ⁿ. What is n?
  14. 14.Write (5⁹)⁷ as a single power 5ⁿ. What is n?
  15. 15.Write (4⁸)⁵ as a single power 4ⁿ. What is n?
  16. 16.What is the value of (1/6)⁻²? =
  17. 17.Write 2⁴ × 2² as a single power 2ⁿ. What is n?
  18. 18.What is the value of 3⁻⁴ (as a fraction)? =
  19. 19.Write (4⁵)⁸ as a single power 4ⁿ. What is n?
  20. 20.What is the value of 5¹ × 5⁻⁴? =
  21. 21.Write 2,300 in standard form as 2.3 × 10ⁿ. What is n?
  22. 22.What is the value of 2⁴ × 2⁻¹? =
  23. 23.What is the value of 3²? =
  24. 24.Write 1.3 × 10⁻² as a decimal. =
  25. 25.What is the value of 3¹ × 3⁻⁴? =
  26. 26.What is the value of 3⁵? =
  27. 27.What is the value of 4⁵? =
  28. 28.What is the value of 9⁵? =
  29. 29.Write 4¹³ ÷ 4⁸ as a single power 4ⁿ. What is n?
  30. 30.Write 3.5 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 7⁻² (as a fraction)? =
  32. 32.Write 8¹⁰ ÷ 8⁴ as a single power 8ⁿ. What is n?
  33. 33.Write 2.1 × 10⁻⁴ as a decimal. =
  34. 34.What is the value of 10⁻¹ (as a fraction)? =
  35. 35.What is the value of 2¹⁵? =
  36. 36.Write 3,80,00,000 in standard form as 3.8 × 10ⁿ. What is n?
  37. 37.What is the value of 4⁻⁴ (as a fraction)? =
  38. 38.Write 8⁵ × 8⁸ as a single power 8ⁿ. What is n?
  39. 39.What is the value of 10⁻³ (as a fraction)? =
  40. 40.Write 8⁶ × 8² as a single power 8ⁿ. What is n?

Answer key

  1. 13
  2. 81
  3. 0.83
  4. 0.18
  5. 42
  6. 13
  7. 3
  8. 6561
  9. 3
  10. 4
  11. 1/9
  12. 512
  13. 2
  14. 63
  15. 40
  16. 36
  17. 6
  18. 1/81
  19. 40
  20. 1/125
  21. 3
  22. 8
  23. 9
  24. 0.013
  25. 1/27
  26. 243
  27. 1024
  28. 59049
  29. 5
  30. 0.00035
  31. 1/49
  32. 6
  33. 0.00021
  34. 1/10
  35. 32768
  36. 7
  37. 1/256
  38. 13
  39. 1/1000
  40. 8

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