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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 115 · 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 1.9 × 10⁻² as a decimal. =
  2. 2.Write (3⁹)⁹ as a single power 3ⁿ. What is n?
  3. 3.Write (2⁷)⁸ as a single power 2ⁿ. What is n?
  4. 4.Write 1.7 × 10⁻⁴ as a decimal. =
  5. 5.Write 2,20,00,000 in standard form as 2.2 × 10ⁿ. What is n?
  6. 6.What is the value of 4⁻⁴ (as a fraction)? =
  7. 7.What is the value of (3/7)⁻²? =
  8. 8.Write 8.6 × 10⁻¹ as a decimal. =
  9. 9.Write 8³ × 8² as a single power 8ⁿ. What is n?
  10. 10.What is the value of 2⁶ × 2⁻⁴? =
  11. 11.What is the value of 5⁶ × 5⁻³? =
  12. 12.Write 3.9 × 10⁻¹ as a decimal. =
  13. 13.What is the value of 2⁵ × 2⁻³? =
  14. 14.Write 3.4 × 10⁻¹ as a decimal. =
  15. 15.What is the value of 5⁻³ (as a fraction)? =
  16. 16.9.7 × 10⁴ =
  17. 17.2.4 × 10² =
  18. 18.Write 4 × 10⁻⁴ as a decimal. =
  19. 19.Write 8.8 × 10⁻³ as a decimal. =
  20. 20.What is the value of (1/6)⁻¹? =
  21. 21.Write 6⁶ × 6⁹ as a single power 6ⁿ. What is n?
  22. 22.Write 2.9 × 10⁻⁴ as a decimal. =
  23. 23.Write 9,100 in standard form as 9.1 × 10ⁿ. What is n?
  24. 24.Write 4.9 × 10⁻³ as a decimal. =
  25. 25.Write 6¹³ ÷ 6⁴ as a single power 6ⁿ. What is n?
  26. 26.What is the value of 3¹⁰? =
  27. 27.What is the value of (3/4)⁻²? =
  28. 28.What is the value of 10¹ × 10⁻³? =
  29. 29.Write (9³)³ as a single power 9ⁿ. What is n?
  30. 30.Write 7,900 in standard form as 7.9 × 10ⁿ. What is n?
  31. 31.Write 5⁷ ÷ 5³ as a single power 5ⁿ. What is n?
  32. 32.Write 910 in standard form as 9.1 × 10ⁿ. What is n?
  33. 33.What is the value of 5¹ × 5⁻²? =
  34. 34.Write 3.5 × 10⁻¹ as a decimal. =
  35. 35.What is the value of 10⁻³ (as a fraction)? =
  36. 36.2.2 × 10⁴ =
  37. 37.What is the value of (1/5)⁻²? =
  38. 38.What is the value of 5³ × 5⁻²? =
  39. 39.What is the value of 3² × 3⁻⁵? =
  40. 40.What is the value of 2¹¹? =

Answer key

  1. 0.019
  2. 81
  3. 56
  4. 0.00017
  5. 7
  6. 1/256
  7. 49/9
  8. 0.86
  9. 5
  10. 4
  11. 125
  12. 0.39
  13. 4
  14. 0.34
  15. 1/125
  16. 97000
  17. 240
  18. 0.0004
  19. 0.0088
  20. 6
  21. 15
  22. 0.00029
  23. 3
  24. 0.0049
  25. 9
  26. 59049
  27. 16/9
  28. 1/100
  29. 9
  30. 3
  31. 4
  32. 2
  33. 1/5
  34. 0.35
  35. 1/1000
  36. 22000
  37. 25
  38. 5
  39. 1/27
  40. 2048

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