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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 389 · 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 3¹¹ ÷ 3⁶ as a single power 3ⁿ. What is n?
  2. 2.Write 1.5 × 10⁻⁴ as a decimal. =
  3. 3.Write 9⁸ × 9⁸ as a single power 9ⁿ. What is n?
  4. 4.What is the value of 2¹³? =
  5. 5.Write 3¹¹ ÷ 3⁸ as a single power 3ⁿ. What is n?
  6. 6.What is the value of 5⁻³ (as a fraction)? =
  7. 7.What is the value of 5⁴ × 5⁻⁶? =
  8. 8.What is the value of 5⁶ × 5⁻⁶? =
  9. 9.Write 5,100 in standard form as 5.1 × 10ⁿ. What is n?
  10. 10.Write 4 × 10⁻¹ as a decimal. =
  11. 11.What is the value of 8⁵? =
  12. 12.Write 9.8 × 10⁻² as a decimal. =
  13. 13.What is the value of 2⁻⁵ (as a fraction)? =
  14. 14.What is the value of 3¹ × 3⁻⁵? =
  15. 15.Write 2.6 × 10⁻¹ as a decimal. =
  16. 16.What is the value of 3⁻⁵ (as a fraction)? =
  17. 17.What is the value of 2⁴? =
  18. 18.Write 7.8 × 10⁻⁴ as a decimal. =
  19. 19.What is the value of 5⁶? =
  20. 20.Write 3,30,000 in standard form as 3.3 × 10ⁿ. What is n?
  21. 21.What is the value of 2³ × 2⁻³? =
  22. 22.What is the value of 3⁻² (as a fraction)? =
  23. 23.Write 8.8 × 10⁻¹ as a decimal. =
  24. 24.What is the value of (7/8)⁻¹? =
  25. 25.What is the value of 4⁷? =
  26. 26.Write 7.4 × 10⁻¹ as a decimal. =
  27. 27.What is the value of 2⁻⁴ (as a fraction)? =
  28. 28.What is the value of (8/9)⁻²? =
  29. 29.What is the value of 2⁶ × 2⁻²? =
  30. 30.Write 2,50,000 in standard form as 2.5 × 10ⁿ. What is n?
  31. 31.What is the value of (2/5)⁻¹? =
  32. 32.What is the value of 6⁵? =
  33. 33.What is the value of 2¹⁴? =
  34. 34.Write 8.8 × 10⁻³ as a decimal. =
  35. 35.What is the value of 6⁶? =
  36. 36.What is the value of (1/2)⁻¹? =
  37. 37.Write 3,20,00,000 in standard form as 3.2 × 10ⁿ. What is n?
  38. 38.1.3 × 10³ =
  39. 39.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  40. 40.What is the value of 5⁵ × 5⁻¹? =

Answer key

  1. 5
  2. 0.00015
  3. 16
  4. 8192
  5. 3
  6. 1/125
  7. 1/25
  8. 1
  9. 3
  10. 0.4
  11. 32768
  12. 0.098
  13. 1/32
  14. 1/81
  15. 0.26
  16. 1/243
  17. 16
  18. 0.00078
  19. 15625
  20. 5
  21. 1
  22. 1/9
  23. 0.88
  24. 8/7
  25. 16384
  26. 0.74
  27. 1/16
  28. 81/64
  29. 16
  30. 5
  31. 5/2
  32. 7776
  33. 16384
  34. 0.0088
  35. 46656
  36. 2
  37. 7
  38. 1300
  39. 9
  40. 625

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