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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 145 · 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 830 in standard form as 8.3 × 10ⁿ. What is n?
  2. 2.What is the value of 8⁻¹ (as a fraction)? =
  3. 3.What is the value of 2⁴? =
  4. 4.What is the value of 7⁻¹ (as a fraction)? =
  5. 5.What is the value of 5⁻² (as a fraction)? =
  6. 6.Write 2² × 2⁹ as a single power 2ⁿ. What is n?
  7. 7.Write 5.3 × 10⁻¹ as a decimal. =
  8. 8.What is the value of 2¹²? =
  9. 9.What is the value of 5² × 5⁻⁵? =
  10. 10.Write 5,10,000 in standard form as 5.1 × 10ⁿ. What is n?
  11. 11.Write 1.5 × 10⁻² as a decimal. =
  12. 12.Write (9⁶)³ as a single power 9ⁿ. What is n?
  13. 13.Write 2¹² ÷ 2⁷ as a single power 2ⁿ. What is n?
  14. 14.What is the value of 2¹⁵? =
  15. 15.What is the value of (8/9)⁻¹? =
  16. 16.What is the value of (3/5)⁻¹? =
  17. 17.Write 4.1 × 10⁻³ as a decimal. =
  18. 18.What is the value of 2⁻² (as a fraction)? =
  19. 19.What is the value of 2⁻⁸ (as a fraction)? =
  20. 20.Write 65,00,000 in standard form as 6.5 × 10ⁿ. What is n?
  21. 21.What is the value of 6⁴? =
  22. 22.What is the value of (5/7)⁻²? =
  23. 23.What is the value of 2² × 2⁻⁶? =
  24. 24.What is the value of 2⁻⁹ (as a fraction)? =
  25. 25.What is the value of 8³? =
  26. 26.Write 1,400 in standard form as 1.4 × 10ⁿ. What is n?
  27. 27.What is the value of (3/8)⁻¹? =
  28. 28.What is the value of 3⁴ × 3⁻¹? =
  29. 29.Write (3⁷)⁸ as a single power 3ⁿ. What is n?
  30. 30.Write 7.7 × 10⁻² as a decimal. =
  31. 31.What is the value of 3¹ × 3⁻⁵? =
  32. 32.What is the value of 10⁵ × 10⁻²? =
  33. 33.What is the value of 3² × 3⁻⁴? =
  34. 34.2.4 × 10³ =
  35. 35.Write 6⁷ × 6⁷ as a single power 6ⁿ. What is n?
  36. 36.Write 4,600 in standard form as 4.6 × 10ⁿ. What is n?
  37. 37.Write 1.3 × 10⁻¹ as a decimal. =
  38. 38.Write 4.2 × 10⁻³ as a decimal. =
  39. 39.Write 9⁸ × 9³ as a single power 9ⁿ. What is n?
  40. 40.4.2 × 10² =

Answer key

  1. 2
  2. 1/8
  3. 16
  4. 1/7
  5. 1/25
  6. 11
  7. 0.53
  8. 4096
  9. 1/125
  10. 5
  11. 0.015
  12. 18
  13. 5
  14. 32768
  15. 9/8
  16. 5/3
  17. 0.0041
  18. 1/4
  19. 1/256
  20. 6
  21. 1296
  22. 49/25
  23. 1/16
  24. 1/512
  25. 512
  26. 3
  27. 8/3
  28. 27
  29. 56
  30. 0.077
  31. 1/81
  32. 1000
  33. 1/9
  34. 2400
  35. 14
  36. 3
  37. 0.13
  38. 0.0042
  39. 11
  40. 420

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