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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 443 · 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 7,900 in standard form as 7.9 × 10ⁿ. What is n?
  2. 2.Write 5⁵ × 5³ as a single power 5ⁿ. What is n?
  3. 3.What is the value of 2⁶ × 2⁻¹? =
  4. 4.Write 6⁷ × 6⁶ as a single power 6ⁿ. What is n?
  5. 5.What is the value of 3⁵ × 3⁻⁵? =
  6. 6.Write (9²)⁵ as a single power 9ⁿ. What is n?
  7. 7.What is the value of 2¹⁵? =
  8. 8.Write 1.5 × 10⁻⁴ as a decimal. =
  9. 9.What is the value of 10² × 10⁻⁵? =
  10. 10.What is the value of 5⁶ × 5⁻¹? =
  11. 11.What is the value of (4/5)⁻²? =
  12. 12.Write 5,600 in standard form as 5.6 × 10ⁿ. What is n?
  13. 13.Write 6.1 × 10⁻⁴ as a decimal. =
  14. 14.Write 51,000 in standard form as 5.1 × 10ⁿ. What is n?
  15. 15.What is the value of 4⁴? =
  16. 16.What is the value of 2⁻¹ (as a fraction)? =
  17. 17.Write 6¹³ ÷ 6⁷ as a single power 6ⁿ. What is n?
  18. 18.Write 7¹⁰ ÷ 7⁷ as a single power 7ⁿ. What is n?
  19. 19.What is the value of 5⁵ × 5⁻⁴? =
  20. 20.What is the value of 3² × 3⁻²? =
  21. 21.Write (5⁶)⁷ as a single power 5ⁿ. What is n?
  22. 22.Write 5.7 × 10⁻² as a decimal. =
  23. 23.5.4 × 10³ =
  24. 24.What is the value of (3/7)⁻¹? =
  25. 25.What is the value of 2³? =
  26. 26.What is the value of (1/6)⁻²? =
  27. 27.What is the value of 3⁶ × 3⁻¹? =
  28. 28.Write 880 in standard form as 8.8 × 10ⁿ. What is n?
  29. 29.Write 5.5 × 10⁻² as a decimal. =
  30. 30.Write 3¹³ ÷ 3⁶ as a single power 3ⁿ. What is n?
  31. 31.What is the value of 2⁵ × 2⁻¹? =
  32. 32.Write 7 × 10⁻⁴ as a decimal. =
  33. 33.What is the value of 2⁹? =
  34. 34.What is the value of 2⁵ × 2⁻²? =
  35. 35.Write 5.2 × 10⁻⁴ as a decimal. =
  36. 36.What is the value of 3⁻⁶ (as a fraction)? =
  37. 37.Write 2.6 × 10⁻³ as a decimal. =
  38. 38.Write 4⁹ ÷ 4⁵ as a single power 4ⁿ. What is n?
  39. 39.Write 5 × 10⁻² as a decimal. =
  40. 40.6 × 10⁶ =

Answer key

  1. 3
  2. 8
  3. 32
  4. 13
  5. 1
  6. 10
  7. 32768
  8. 0.00015
  9. 1/1000
  10. 3125
  11. 25/16
  12. 3
  13. 0.00061
  14. 4
  15. 256
  16. 1/2
  17. 6
  18. 3
  19. 5
  20. 1
  21. 42
  22. 0.057
  23. 5400
  24. 7/3
  25. 8
  26. 36
  27. 243
  28. 2
  29. 0.055
  30. 7
  31. 16
  32. 0.0007
  33. 512
  34. 8
  35. 0.00052
  36. 1/729
  37. 0.0026
  38. 4
  39. 0.05
  40. 6000000

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