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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 663 · 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.What is the value of 2⁻³ (as a fraction)? =
  2. 2.Write (9⁴)⁴ as a single power 9ⁿ. What is n?
  3. 3.Write (4³)⁹ as a single power 4ⁿ. What is n?
  4. 4.What is the value of (5/8)⁻²? =
  5. 5.What is the value of 8²? =
  6. 6.What is the value of 3¹ × 3⁻²? =
  7. 7.2 × 10⁷ =
  8. 8.8.4 × 10⁵ =
  9. 9.Write 5,70,00,000 in standard form as 5.7 × 10ⁿ. What is n?
  10. 10.Write 75,00,000 in standard form as 7.5 × 10ⁿ. What is n?
  11. 11.Write 9¹⁰ ÷ 9³ as a single power 9ⁿ. What is n?
  12. 12.What is the value of 6⁻³ (as a fraction)? =
  13. 13.What is the value of 4⁵? =
  14. 14.What is the value of 2⁵? =
  15. 15.Write (4²)⁶ as a single power 4ⁿ. What is n?
  16. 16.Write 1.2 × 10⁻⁴ as a decimal. =
  17. 17.What is the value of 3⁴ × 3⁻⁴? =
  18. 18.Write 8.3 × 10⁻¹ as a decimal. =
  19. 19.Write 6⁶ × 6⁷ as a single power 6ⁿ. What is n?
  20. 20.Write 7.3 × 10⁻² as a decimal. =
  21. 21.5.4 × 10⁵ =
  22. 22.What is the value of 3⁻² (as a fraction)? =
  23. 23.What is the value of 7³? =
  24. 24.What is the value of 3⁶ × 3⁻²? =
  25. 25.What is the value of 4⁻¹ (as a fraction)? =
  26. 26.What is the value of 5³ × 5⁻¹? =
  27. 27.Write 7.7 × 10⁻³ as a decimal. =
  28. 28.What is the value of 5⁶ × 5⁻⁵? =
  29. 29.Write 3⁴ × 3⁴ as a single power 3ⁿ. What is n?
  30. 30.7.3 × 10⁷ =
  31. 31.Write (4⁶)³ as a single power 4ⁿ. What is n?
  32. 32.Write 2² × 2⁷ as a single power 2ⁿ. What is n?
  33. 33.What is the value of 10¹ × 10⁻³? =
  34. 34.What is the value of 3³ × 3⁻¹? =
  35. 35.Write (9⁷)⁷ as a single power 9ⁿ. What is n?
  36. 36.Write 900 in standard form as 9 × 10ⁿ. What is n?
  37. 37.Write (4⁵)⁶ as a single power 4ⁿ. What is n?
  38. 38.What is the value of 3³? =
  39. 39.What is the value of 4⁷? =
  40. 40.Write 4¹² ÷ 4⁹ as a single power 4ⁿ. What is n?

Answer key

  1. 1/8
  2. 16
  3. 27
  4. 64/25
  5. 64
  6. 1/3
  7. 20000000
  8. 840000
  9. 7
  10. 6
  11. 7
  12. 1/216
  13. 1024
  14. 32
  15. 12
  16. 0.00012
  17. 1
  18. 0.83
  19. 13
  20. 0.073
  21. 540000
  22. 1/9
  23. 343
  24. 81
  25. 1/4
  26. 25
  27. 0.0077
  28. 5
  29. 8
  30. 73000000
  31. 18
  32. 9
  33. 1/100
  34. 9
  35. 49
  36. 2
  37. 30
  38. 27
  39. 16384
  40. 3

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