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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 716 · 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 9⁵ × 9⁸ as a single power 9ⁿ. What is n?
  2. 2.What is the value of 3⁸? =
  3. 3.Write (6⁴)² as a single power 6ⁿ. What is n?
  4. 4.What is the value of (1/2)⁻²? =
  5. 5.What is the value of 3⁴ × 3⁻⁶? =
  6. 6.Write 2¹⁰ ÷ 2⁴ as a single power 2ⁿ. What is n?
  7. 7.What is the value of 3⁴ × 3⁻³? =
  8. 8.What is the value of 6²? =
  9. 9.What is the value of 2² × 2⁻⁵? =
  10. 10.Write 300 in standard form as 3 × 10ⁿ. What is n?
  11. 11.What is the value of 2⁵ × 2⁻¹? =
  12. 12.What is the value of 2⁹? =
  13. 13.What is the value of 2⁷? =
  14. 14.What is the value of 7⁻³ (as a fraction)? =
  15. 15.What is the value of 5⁶? =
  16. 16.Write (6²)² as a single power 6ⁿ. What is n?
  17. 17.Write 630 in standard form as 6.3 × 10ⁿ. What is n?
  18. 18.Write 9¹³ ÷ 9⁹ as a single power 9ⁿ. What is n?
  19. 19.What is the value of 2¹¹? =
  20. 20.Write 7 × 10⁻⁴ as a decimal. =
  21. 21.Write (3²)⁴ as a single power 3ⁿ. What is n?
  22. 22.What is the value of 3⁶ × 3⁻⁵? =
  23. 23.What is the value of 5⁶ × 5⁻¹? =
  24. 24.What is the value of 7⁻¹ (as a fraction)? =
  25. 25.2.2 × 10⁶ =
  26. 26.1.9 × 10² =
  27. 27.What is the value of (3/4)⁻¹? =
  28. 28.What is the value of 3⁻² (as a fraction)? =
  29. 29.Write 2.4 × 10⁻¹ as a decimal. =
  30. 30.1.6 × 10⁶ =
  31. 31.Write 3.4 × 10⁻³ as a decimal. =
  32. 32.What is the value of 5⁵ × 5⁻³? =
  33. 33.Write (7³)² as a single power 7ⁿ. What is n?
  34. 34.Write 1.6 × 10⁻⁴ as a decimal. =
  35. 35.What is the value of 10⁶ × 10⁻³? =
  36. 36.1.2 × 10³ =
  37. 37.What is the value of 3³ × 3⁻³? =
  38. 38.1.4 × 10² =
  39. 39.What is the value of (1/6)⁻²? =
  40. 40.What is the value of 5² × 5⁻⁴? =

Answer key

  1. 13
  2. 6561
  3. 8
  4. 4
  5. 1/9
  6. 6
  7. 3
  8. 36
  9. 1/8
  10. 2
  11. 16
  12. 512
  13. 128
  14. 1/343
  15. 15625
  16. 4
  17. 2
  18. 4
  19. 2048
  20. 0.0007
  21. 8
  22. 3
  23. 3125
  24. 1/7
  25. 2200000
  26. 190
  27. 4/3
  28. 1/9
  29. 0.24
  30. 1600000
  31. 0.0034
  32. 25
  33. 6
  34. 0.00016
  35. 1000
  36. 1200
  37. 1
  38. 140
  39. 36
  40. 1/25

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