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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 675 · 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 5² × 5⁻⁶? =
  2. 2.What is the value of 2¹ × 2⁻²? =
  3. 3.What is the value of 2⁶ × 2⁻¹? =
  4. 4.Write 14,000 in standard form as 1.4 × 10ⁿ. What is n?
  5. 5.Write 3.3 × 10⁻⁴ as a decimal. =
  6. 6.What is the value of 2¹⁵? =
  7. 7.What is the value of 2⁴ × 2⁻⁶? =
  8. 8.Write (8³)⁸ as a single power 8ⁿ. What is n?
  9. 9.1.4 × 10² =
  10. 10.Write (5⁵)⁴ as a single power 5ⁿ. What is n?
  11. 11.What is the value of 2¹⁰? =
  12. 12.What is the value of (2/9)⁻¹? =
  13. 13.Write 6⁷ × 6⁵ as a single power 6ⁿ. What is n?
  14. 14.Write 3⁴ × 3⁸ as a single power 3ⁿ. What is n?
  15. 15.Write 8² × 8⁶ as a single power 8ⁿ. What is n?
  16. 16.What is the value of (4/7)⁻¹? =
  17. 17.Write 7⁵ × 7⁸ as a single power 7ⁿ. What is n?
  18. 18.What is the value of (1/4)⁻¹? =
  19. 19.What is the value of 6⁶? =
  20. 20.4.1 × 10⁷ =
  21. 21.Write 2.8 × 10⁻⁴ as a decimal. =
  22. 22.What is the value of (1/8)⁻²? =
  23. 23.What is the value of (3/5)⁻¹? =
  24. 24.Write 5⁹ ÷ 5⁴ as a single power 5ⁿ. What is n?
  25. 25.Write 3¹¹ ÷ 3⁶ as a single power 3ⁿ. What is n?
  26. 26.What is the value of 3³? =
  27. 27.What is the value of 2⁴? =
  28. 28.Write 9⁸ × 9⁶ as a single power 9ⁿ. What is n?
  29. 29.Write 3.7 × 10⁻³ as a decimal. =
  30. 30.Write 560 in standard form as 5.6 × 10ⁿ. What is n?
  31. 31.What is the value of 3⁻¹ (as a fraction)? =
  32. 32.Write (2⁴)⁷ as a single power 2ⁿ. What is n?
  33. 33.What is the value of (1/3)⁻¹? =
  34. 34.What is the value of 5¹ × 5⁻¹? =
  35. 35.What is the value of 10²? =
  36. 36.What is the value of 2⁻⁵ (as a fraction)? =
  37. 37.What is the value of 7⁴? =
  38. 38.7.7 × 10⁶ =
  39. 39.1.5 × 10² =
  40. 40.Write 2 × 10⁻² as a decimal. =

Answer key

  1. 1/625
  2. 1/2
  3. 32
  4. 4
  5. 0.00033
  6. 32768
  7. 1/4
  8. 24
  9. 140
  10. 20
  11. 1024
  12. 9/2
  13. 12
  14. 12
  15. 8
  16. 7/4
  17. 13
  18. 4
  19. 46656
  20. 41000000
  21. 0.00028
  22. 64
  23. 5/3
  24. 5
  25. 5
  26. 27
  27. 16
  28. 14
  29. 0.0037
  30. 2
  31. 1/3
  32. 28
  33. 3
  34. 1
  35. 100
  36. 1/32
  37. 2401
  38. 7700000
  39. 150
  40. 0.02

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