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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 598 · 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 (6⁶)⁸ as a single power 6ⁿ. What is n?
  2. 2.6.9 × 10⁴ =
  3. 3.What is the value of 5¹ × 5⁻⁴? =
  4. 4.What is the value of 2³? =
  5. 5.What is the value of 10¹ × 10⁻²? =
  6. 6.What is the value of (4/9)⁻²? =
  7. 7.What is the value of 5⁵? =
  8. 8.What is the value of 5⁶? =
  9. 9.Write (5⁹)⁶ as a single power 5ⁿ. What is n?
  10. 10.What is the value of (4/7)⁻¹? =
  11. 11.Write 3⁵ × 3⁶ as a single power 3ⁿ. What is n?
  12. 12.What is the value of 2⁴ × 2⁻⁴? =
  13. 13.What is the value of 2¹¹? =
  14. 14.What is the value of 5⁻⁴ (as a fraction)? =
  15. 15.Write 9,10,000 in standard form as 9.1 × 10ⁿ. What is n?
  16. 16.What is the value of 3¹ × 3⁻³? =
  17. 17.Write 5⁴ × 5⁶ as a single power 5ⁿ. What is n?
  18. 18.Write 6 × 10⁻¹ as a decimal. =
  19. 19.What is the value of 2² × 2⁻²? =
  20. 20.Write 1.5 × 10⁻¹ as a decimal. =
  21. 21.What is the value of 2⁻¹ (as a fraction)? =
  22. 22.Write 2⁵ × 2² as a single power 2ⁿ. What is n?
  23. 23.Write 3⁵ × 3⁴ as a single power 3ⁿ. What is n?
  24. 24.7.5 × 10³ =
  25. 25.What is the value of 5⁻² (as a fraction)? =
  26. 26.7.7 × 10⁴ =
  27. 27.What is the value of 5² × 5⁻¹? =
  28. 28.What is the value of 2¹ × 2⁻⁵? =
  29. 29.5 × 10² =
  30. 30.Write 9.2 × 10⁻⁴ as a decimal. =
  31. 31.What is the value of 5³ × 5⁻²? =
  32. 32.What is the value of 3⁻⁴ (as a fraction)? =
  33. 33.What is the value of 3⁻² (as a fraction)? =
  34. 34.What is the value of (3/7)⁻²? =
  35. 35.Write 8.5 × 10⁻¹ as a decimal. =
  36. 36.What is the value of 9⁻² (as a fraction)? =
  37. 37.Write 3.6 × 10⁻¹ as a decimal. =
  38. 38.What is the value of 6⁻³ (as a fraction)? =
  39. 39.Write 4² × 4² as a single power 4ⁿ. What is n?
  40. 40.Write 4 × 10⁻² as a decimal. =

Answer key

  1. 48
  2. 69000
  3. 1/125
  4. 8
  5. 1/10
  6. 81/16
  7. 3125
  8. 15625
  9. 54
  10. 7/4
  11. 11
  12. 1
  13. 2048
  14. 1/625
  15. 5
  16. 1/9
  17. 10
  18. 0.6
  19. 1
  20. 0.15
  21. 1/2
  22. 7
  23. 9
  24. 7500
  25. 1/25
  26. 77000
  27. 5
  28. 1/16
  29. 500
  30. 0.00092
  31. 5
  32. 1/81
  33. 1/9
  34. 49/9
  35. 0.85
  36. 1/81
  37. 0.36
  38. 1/216
  39. 4
  40. 0.04

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