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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 164 · 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 3,400 in standard form as 3.4 × 10ⁿ. What is n?
  2. 2.Write 4² × 4⁸ as a single power 4ⁿ. What is n?
  3. 3.Write 3⁷ × 3² as a single power 3ⁿ. What is n?
  4. 4.What is the value of 2⁻⁴ (as a fraction)? =
  5. 5.Write 2² × 2⁵ as a single power 2ⁿ. What is n?
  6. 6.What is the value of 3¹⁰? =
  7. 7.Write 2⁵ × 2⁷ as a single power 2ⁿ. What is n?
  8. 8.What is the value of 5⁶ × 5⁻²? =
  9. 9.What is the value of 3⁸? =
  10. 10.2.2 × 10⁴ =
  11. 11.Write 4,90,00,000 in standard form as 4.9 × 10ⁿ. What is n?
  12. 12.Write 9.7 × 10⁻⁴ as a decimal. =
  13. 13.What is the value of 5¹ × 5⁻²? =
  14. 14.What is the value of 2⁴ × 2⁻²? =
  15. 15.Write 6¹² ÷ 6³ as a single power 6ⁿ. What is n?
  16. 16.What is the value of 2¹⁰? =
  17. 17.Write 6,200 in standard form as 6.2 × 10ⁿ. What is n?
  18. 18.What is the value of 2⁶ × 2⁻⁶? =
  19. 19.What is the value of 5² × 5⁻⁶? =
  20. 20.Write 3,50,000 in standard form as 3.5 × 10ⁿ. What is n?
  21. 21.What is the value of 2⁵? =
  22. 22.What is the value of 2⁻⁵ (as a fraction)? =
  23. 23.Write 6,40,00,000 in standard form as 6.4 × 10ⁿ. What is n?
  24. 24.What is the value of 2² × 2⁻⁶? =
  25. 25.What is the value of 10⁶ × 10⁻¹? =
  26. 26.8.1 × 10⁴ =
  27. 27.Write 93,00,000 in standard form as 9.3 × 10ⁿ. What is n?
  28. 28.What is the value of (2/9)⁻²? =
  29. 29.What is the value of (3/8)⁻¹? =
  30. 30.Write (4⁴)⁷ as a single power 4ⁿ. What is n?
  31. 31.What is the value of 3² × 3⁻⁴? =
  32. 32.Write 9.7 × 10⁻¹ as a decimal. =
  33. 33.Write 6⁹ ÷ 6⁶ as a single power 6ⁿ. What is n?
  34. 34.1.8 × 10⁵ =
  35. 35.What is the value of 9⁻² (as a fraction)? =
  36. 36.What is the value of 5¹ × 5⁻⁵? =
  37. 37.Write 6⁷ × 6⁸ as a single power 6ⁿ. What is n?
  38. 38.What is the value of 4²? =
  39. 39.Write 6.5 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of 10⁵ × 10⁻³? =

Answer key

  1. 3
  2. 10
  3. 9
  4. 1/16
  5. 7
  6. 59049
  7. 12
  8. 625
  9. 6561
  10. 22000
  11. 7
  12. 0.00097
  13. 1/5
  14. 4
  15. 9
  16. 1024
  17. 3
  18. 1
  19. 1/625
  20. 5
  21. 32
  22. 1/32
  23. 7
  24. 1/16
  25. 100000
  26. 81000
  27. 6
  28. 81/4
  29. 8/3
  30. 28
  31. 1/9
  32. 0.97
  33. 3
  34. 180000
  35. 1/81
  36. 1/625
  37. 15
  38. 16
  39. 0.00065
  40. 100

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