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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 220 · 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 8⁹ × 8² as a single power 8ⁿ. What is n?
  2. 2.Write (4⁵)⁷ as a single power 4ⁿ. What is n?
  3. 3.What is the value of 5¹ × 5⁻¹? =
  4. 4.What is the value of 7⁻¹ (as a fraction)? =
  5. 5.What is the value of 2² × 2⁻⁶? =
  6. 6.What is the value of 2⁸? =
  7. 7.Write 2.5 × 10⁻⁴ as a decimal. =
  8. 8.Write 6.7 × 10⁻¹ as a decimal. =
  9. 9.Write (4⁹)⁷ as a single power 4ⁿ. What is n?
  10. 10.What is the value of 7⁻³ (as a fraction)? =
  11. 11.Write 5.5 × 10⁻¹ as a decimal. =
  12. 12.Write 5.5 × 10⁻² as a decimal. =
  13. 13.4.1 × 10² =
  14. 14.Write 2¹³ ÷ 2⁷ as a single power 2ⁿ. What is n?
  15. 15.1.4 × 10⁶ =
  16. 16.Write 2.3 × 10⁻¹ as a decimal. =
  17. 17.What is the value of 7⁻² (as a fraction)? =
  18. 18.What is the value of 3⁸? =
  19. 19.Write (9³)⁴ as a single power 9ⁿ. What is n?
  20. 20.What is the value of 3⁴ × 3⁻¹? =
  21. 21.Write 4.2 × 10⁻¹ as a decimal. =
  22. 22.Write 5.1 × 10⁻³ as a decimal. =
  23. 23.What is the value of 3⁵ × 3⁻⁵? =
  24. 24.Write 2.7 × 10⁻¹ as a decimal. =
  25. 25.What is the value of (8/9)⁻²? =
  26. 26.What is the value of 2² × 2⁻²? =
  27. 27.Write 4 × 10⁻² as a decimal. =
  28. 28.What is the value of 2¹⁴? =
  29. 29.Write 3⁷ × 3² as a single power 3ⁿ. What is n?
  30. 30.Write 8.1 × 10⁻² as a decimal. =
  31. 31.What is the value of (1/9)⁻²? =
  32. 32.Write 5⁹ ÷ 5³ as a single power 5ⁿ. What is n?
  33. 33.What is the value of (3/8)⁻¹? =
  34. 34.What is the value of 2⁻¹ (as a fraction)? =
  35. 35.Write 8⁷ × 8³ as a single power 8ⁿ. What is n?
  36. 36.Write (2⁵)³ as a single power 2ⁿ. What is n?
  37. 37.Write 610 in standard form as 6.1 × 10ⁿ. What is n?
  38. 38.What is the value of 2⁻⁴ (as a fraction)? =
  39. 39.Write (8⁵)² as a single power 8ⁿ. What is n?
  40. 40.What is the value of 3⁵ × 3⁻³? =

Answer key

  1. 11
  2. 35
  3. 1
  4. 1/7
  5. 1/16
  6. 256
  7. 0.00025
  8. 0.67
  9. 63
  10. 1/343
  11. 0.55
  12. 0.055
  13. 410
  14. 6
  15. 1400000
  16. 0.23
  17. 1/49
  18. 6561
  19. 12
  20. 27
  21. 0.42
  22. 0.0051
  23. 1
  24. 0.27
  25. 81/64
  26. 1
  27. 0.04
  28. 16384
  29. 9
  30. 0.081
  31. 81
  32. 6
  33. 8/3
  34. 1/2
  35. 10
  36. 15
  37. 2
  38. 1/16
  39. 10
  40. 9

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