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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 89 · 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 3.4 × 10⁻⁴ as a decimal. =
  2. 2.5.5 × 10⁶ =
  3. 3.What is the value of 2⁻² (as a fraction)? =
  4. 4.What is the value of 5³ × 5⁻⁵? =
  5. 5.Write 3² × 3⁵ as a single power 3ⁿ. What is n?
  6. 6.Write 2.1 × 10⁻³ as a decimal. =
  7. 7.Write 5¹³ ÷ 5⁷ as a single power 5ⁿ. What is n?
  8. 8.Write 6³ × 6⁸ as a single power 6ⁿ. What is n?
  9. 9.Write (6²)⁸ as a single power 6ⁿ. What is n?
  10. 10.Write 5⁵ × 5⁷ as a single power 5ⁿ. What is n?
  11. 11.Write (6⁷)⁸ as a single power 6ⁿ. What is n?
  12. 12.Write (2⁹)² as a single power 2ⁿ. What is n?
  13. 13.Write 9⁸ × 9⁶ as a single power 9ⁿ. What is n?
  14. 14.Write 5² × 5² as a single power 5ⁿ. What is n?
  15. 15.Write (7⁶)⁸ as a single power 7ⁿ. What is n?
  16. 16.What is the value of 3⁶ × 3⁻⁴? =
  17. 17.What is the value of (3/5)⁻²? =
  18. 18.What is the value of 10⁻¹ (as a fraction)? =
  19. 19.Write 4⁷ ÷ 4² as a single power 4ⁿ. What is n?
  20. 20.What is the value of (2/5)⁻¹? =
  21. 21.What is the value of (3/8)⁻¹? =
  22. 22.6.2 × 10⁶ =
  23. 23.Write 9⁷ × 9⁴ as a single power 9ⁿ. What is n?
  24. 24.Write 9 × 10⁻⁴ as a decimal. =
  25. 25.What is the value of 2⁻⁵ (as a fraction)? =
  26. 26.What is the value of 2¹ × 2⁻⁵? =
  27. 27.What is the value of 5⁵? =
  28. 28.What is the value of (8/9)⁻¹? =
  29. 29.Write 4.2 × 10⁻⁴ as a decimal. =
  30. 30.Write (7⁵)⁶ as a single power 7ⁿ. What is n?
  31. 31.What is the value of 2⁶ × 2⁻³? =
  32. 32.What is the value of 2⁻¹ (as a fraction)? =
  33. 33.What is the value of 6⁻² (as a fraction)? =
  34. 34.What is the value of 3⁵ × 3⁻⁵? =
  35. 35.Write (4⁵)³ as a single power 4ⁿ. What is n?
  36. 36.Write 8¹¹ ÷ 8⁹ as a single power 8ⁿ. What is n?
  37. 37.Write 9.1 × 10⁻³ as a decimal. =
  38. 38.What is the value of 4⁶? =
  39. 39.What is the value of 4⁻³ (as a fraction)? =
  40. 40.Write (5⁹)⁶ as a single power 5ⁿ. What is n?

Answer key

  1. 0.00034
  2. 5500000
  3. 1/4
  4. 1/25
  5. 7
  6. 0.0021
  7. 6
  8. 11
  9. 16
  10. 12
  11. 56
  12. 18
  13. 14
  14. 4
  15. 48
  16. 9
  17. 25/9
  18. 1/10
  19. 5
  20. 5/2
  21. 8/3
  22. 6200000
  23. 11
  24. 0.0009
  25. 1/32
  26. 1/16
  27. 3125
  28. 9/8
  29. 0.00042
  30. 30
  31. 8
  32. 1/2
  33. 1/36
  34. 1
  35. 15
  36. 2
  37. 0.0091
  38. 4096
  39. 1/64
  40. 54

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