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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 986 · 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 730 in standard form as 7.3 × 10ⁿ. What is n?
  2. 2.Write 770 in standard form as 7.7 × 10ⁿ. What is n?
  3. 3.Write 6⁹ ÷ 6³ as a single power 6ⁿ. What is n?
  4. 4.Write 3¹¹ ÷ 3⁵ as a single power 3ⁿ. What is n?
  5. 5.What is the value of 3³? =
  6. 6.Write 8.5 × 10⁻³ as a decimal. =
  7. 7.What is the value of 2⁸? =
  8. 8.What is the value of 10⁵ × 10⁻²? =
  9. 9.What is the value of 2⁻⁹ (as a fraction)? =
  10. 10.Write 8.5 × 10⁻⁴ as a decimal. =
  11. 11.What is the value of 10⁶ × 10⁻²? =
  12. 12.What is the value of 9⁻² (as a fraction)? =
  13. 13.What is the value of 2⁴? =
  14. 14.Write 9.9 × 10⁻¹ as a decimal. =
  15. 15.Write 3.2 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 3⁷? =
  17. 17.8.4 × 10³ =
  18. 18.Write 9.5 × 10⁻³ as a decimal. =
  19. 19.What is the value of 10³ × 10⁻⁴? =
  20. 20.What is the value of 5⁶ × 5⁻⁶? =
  21. 21.What is the value of 2⁴ × 2⁻⁶? =
  22. 22.What is the value of (8/9)⁻²? =
  23. 23.What is the value of 10⁵? =
  24. 24.What is the value of 9⁻³ (as a fraction)? =
  25. 25.What is the value of 3⁴? =
  26. 26.What is the value of 10⁻³ (as a fraction)? =
  27. 27.What is the value of 3²? =
  28. 28.Write 5.5 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 7³? =
  30. 30.What is the value of (1/9)⁻²? =
  31. 31.What is the value of 2⁹? =
  32. 32.Write 9² × 9⁷ as a single power 9ⁿ. What is n?
  33. 33.Write 2,20,00,000 in standard form as 2.2 × 10ⁿ. What is n?
  34. 34.Write 9⁴ × 9⁸ as a single power 9ⁿ. What is n?
  35. 35.What is the value of 2⁻¹ (as a fraction)? =
  36. 36.Write 9.4 × 10⁻⁴ as a decimal. =
  37. 37.What is the value of 5¹ × 5⁻⁶? =
  38. 38.Write 2.3 × 10⁻² as a decimal. =
  39. 39.What is the value of 7⁵? =
  40. 40.Write 150 in standard form as 1.5 × 10ⁿ. What is n?

Answer key

  1. 2
  2. 2
  3. 6
  4. 6
  5. 27
  6. 0.0085
  7. 256
  8. 1000
  9. 1/512
  10. 0.00085
  11. 10000
  12. 1/81
  13. 16
  14. 0.99
  15. 0.00032
  16. 2187
  17. 8400
  18. 0.0095
  19. 1/10
  20. 1
  21. 1/4
  22. 81/64
  23. 100000
  24. 1/729
  25. 81
  26. 1/1000
  27. 9
  28. 0.55
  29. 343
  30. 81
  31. 512
  32. 9
  33. 7
  34. 12
  35. 1/2
  36. 0.00094
  37. 1/3125
  38. 0.023
  39. 16807
  40. 2

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