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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 923 · 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.What is the value of 5⁴ × 5⁻⁵? =
  2. 2.3 × 10⁷ =
  3. 3.3.6 × 10⁴ =
  4. 4.What is the value of 10⁻¹ (as a fraction)? =
  5. 5.What is the value of 10² × 10⁻²? =
  6. 6.What is the value of 3⁵ × 3⁻¹? =
  7. 7.7.9 × 10³ =
  8. 8.What is the value of 3⁻⁶ (as a fraction)? =
  9. 9.What is the value of 5⁵? =
  10. 10.Write 5¹⁷ ÷ 5⁸ as a single power 5ⁿ. What is n?
  11. 11.Write 32,00,000 in standard form as 3.2 × 10ⁿ. What is n?
  12. 12.What is the value of 3¹⁰? =
  13. 13.What is the value of 7⁻³ (as a fraction)? =
  14. 14.What is the value of 3⁴ × 3⁻⁵? =
  15. 15.What is the value of 7⁴? =
  16. 16.What is the value of 3⁻³ (as a fraction)? =
  17. 17.2.6 × 10⁴ =
  18. 18.Write 69,000 in standard form as 6.9 × 10ⁿ. What is n?
  19. 19.Write 8,200 in standard form as 8.2 × 10ⁿ. What is n?
  20. 20.4.1 × 10⁵ =
  21. 21.Write 430 in standard form as 4.3 × 10ⁿ. What is n?
  22. 22.Write 120 in standard form as 1.2 × 10ⁿ. What is n?
  23. 23.Write 7.7 × 10⁻³ as a decimal. =
  24. 24.What is the value of 2⁹? =
  25. 25.What is the value of (2/9)⁻¹? =
  26. 26.What is the value of 2⁻⁴ (as a fraction)? =
  27. 27.Write 6.2 × 10⁻⁴ as a decimal. =
  28. 28.What is the value of (2/9)⁻²? =
  29. 29.What is the value of 5⁵ × 5⁻⁴? =
  30. 30.What is the value of 5⁶ × 5⁻³? =
  31. 31.7.3 × 10⁴ =
  32. 32.What is the value of 2⁻¹ (as a fraction)? =
  33. 33.Write 2.1 × 10⁻³ as a decimal. =
  34. 34.Write 9.4 × 10⁻² as a decimal. =
  35. 35.Write (4³)⁷ as a single power 4ⁿ. What is n?
  36. 36.7.7 × 10² =
  37. 37.Write (3³)⁴ as a single power 3ⁿ. What is n?
  38. 38.Write 2.8 × 10⁻³ as a decimal. =
  39. 39.Write 4.8 × 10⁻⁴ as a decimal. =
  40. 40.What is the value of 2² × 2⁻⁵? =

Answer key

  1. 1/5
  2. 30000000
  3. 36000
  4. 1/10
  5. 1
  6. 81
  7. 7900
  8. 1/729
  9. 3125
  10. 9
  11. 6
  12. 59049
  13. 1/343
  14. 1/3
  15. 2401
  16. 1/27
  17. 26000
  18. 4
  19. 3
  20. 410000
  21. 2
  22. 2
  23. 0.0077
  24. 512
  25. 9/2
  26. 1/16
  27. 0.00062
  28. 81/4
  29. 5
  30. 125
  31. 73000
  32. 1/2
  33. 0.0021
  34. 0.094
  35. 21
  36. 770
  37. 12
  38. 0.0028
  39. 0.00048
  40. 1/8

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