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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 606 · 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 4¹⁰ ÷ 4⁷ as a single power 4ⁿ. What is n?
  2. 2.Write 7² × 7⁶ as a single power 7ⁿ. What is n?
  3. 3.What is the value of 5² × 5⁻²? =
  4. 4.What is the value of 2⁴ × 2⁻⁶? =
  5. 5.2 × 10² =
  6. 6.What is the value of 2¹ × 2⁻¹? =
  7. 7.Write 5² × 5⁶ as a single power 5ⁿ. What is n?
  8. 8.What is the value of 2³ × 2⁻¹? =
  9. 9.What is the value of 2⁴ × 2⁻²? =
  10. 10.What is the value of 3⁻⁶ (as a fraction)? =
  11. 11.What is the value of 2¹⁴? =
  12. 12.3.2 × 10⁴ =
  13. 13.What is the value of 8²? =
  14. 14.What is the value of 4⁻¹ (as a fraction)? =
  15. 15.5 × 10⁴ =
  16. 16.3.8 × 10² =
  17. 17.What is the value of 2¹⁶? =
  18. 18.Write 2.1 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 3¹⁰? =
  20. 20.What is the value of 2⁷? =
  21. 21.4.7 × 10³ =
  22. 22.What is the value of 10¹ × 10⁻³? =
  23. 23.Write 1.1 × 10⁻³ as a decimal. =
  24. 24.Write 7.3 × 10⁻¹ as a decimal. =
  25. 25.What is the value of 2² × 2⁻³? =
  26. 26.Write 6,60,00,000 in standard form as 6.6 × 10ⁿ. What is n?
  27. 27.Write 2,80,00,000 in standard form as 2.8 × 10ⁿ. What is n?
  28. 28.What is the value of (5/7)⁻²? =
  29. 29.What is the value of 5⁴? =
  30. 30.What is the value of 4⁵? =
  31. 31.What is the value of 2⁴? =
  32. 32.What is the value of 5¹ × 5⁻⁵? =
  33. 33.Write 1.3 × 10⁻⁴ as a decimal. =
  34. 34.What is the value of 2⁻³ (as a fraction)? =
  35. 35.What is the value of 10⁻³ (as a fraction)? =
  36. 36.Write (4⁴)⁹ as a single power 4ⁿ. What is n?
  37. 37.Write 820 in standard form as 8.2 × 10ⁿ. What is n?
  38. 38.What is the value of 7²? =
  39. 39.What is the value of 10³ × 10⁻⁶? =
  40. 40.Write 9.7 × 10⁻¹ as a decimal. =

Answer key

  1. 3
  2. 8
  3. 1
  4. 1/4
  5. 200
  6. 1
  7. 8
  8. 4
  9. 4
  10. 1/729
  11. 16384
  12. 32000
  13. 64
  14. 1/4
  15. 50000
  16. 380
  17. 65536
  18. 0.00021
  19. 59049
  20. 128
  21. 4700
  22. 1/100
  23. 0.0011
  24. 0.73
  25. 1/2
  26. 7
  27. 7
  28. 49/25
  29. 625
  30. 1024
  31. 16
  32. 1/625
  33. 0.00013
  34. 1/8
  35. 1/1000
  36. 36
  37. 2
  38. 49
  39. 1/1000
  40. 0.97

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