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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 302 · 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 (1/2)⁻²? =
  2. 2.What is the value of 5⁶ × 5⁻²? =
  3. 3.Write (4⁷)⁵ as a single power 4ⁿ. What is n?
  4. 4.What is the value of 2¹³? =
  5. 5.Write (7⁷)⁶ as a single power 7ⁿ. What is n?
  6. 6.3.1 × 10⁷ =
  7. 7.What is the value of 2⁴ × 2⁻¹? =
  8. 8.What is the value of 4⁻¹ (as a fraction)? =
  9. 9.What is the value of 2¹²? =
  10. 10.What is the value of 3⁸? =
  11. 11.What is the value of 2⁻⁹ (as a fraction)? =
  12. 12.What is the value of 10¹ × 10⁻²? =
  13. 13.Write 5.2 × 10⁻² as a decimal. =
  14. 14.Write 7,30,00,000 in standard form as 7.3 × 10ⁿ. What is n?
  15. 15.Write 1.6 × 10⁻⁴ as a decimal. =
  16. 16.What is the value of 5⁻¹ (as a fraction)? =
  17. 17.What is the value of 4⁻³ (as a fraction)? =
  18. 18.Write (4³)³ as a single power 4ⁿ. What is n?
  19. 19.What is the value of 3³? =
  20. 20.What is the value of 9⁻² (as a fraction)? =
  21. 21.Write 9.5 × 10⁻² as a decimal. =
  22. 22.6.4 × 10³ =
  23. 23.What is the value of (1/7)⁻²? =
  24. 24.What is the value of 10⁴ × 10⁻⁶? =
  25. 25.What is the value of (2/5)⁻²? =
  26. 26.Write 24,000 in standard form as 2.4 × 10ⁿ. What is n?
  27. 27.What is the value of 3⁵ × 3⁻⁴? =
  28. 28.What is the value of 7⁻¹ (as a fraction)? =
  29. 29.Write 69,00,000 in standard form as 6.9 × 10ⁿ. What is n?
  30. 30.Write (8⁶)⁴ as a single power 8ⁿ. What is n?
  31. 31.Write 3,800 in standard form as 3.8 × 10ⁿ. What is n?
  32. 32.What is the value of 5¹ × 5⁻³? =
  33. 33.What is the value of 7⁴? =
  34. 34.What is the value of (4/5)⁻¹? =
  35. 35.What is the value of 6²? =
  36. 36.What is the value of 10⁻¹ (as a fraction)? =
  37. 37.Write 8⁹ × 8³ as a single power 8ⁿ. What is n?
  38. 38.What is the value of 4²? =
  39. 39.Write 9⁴ × 9⁵ as a single power 9ⁿ. What is n?
  40. 40.What is the value of 5⁵ × 5⁻⁴? =

Answer key

  1. 4
  2. 625
  3. 35
  4. 8192
  5. 42
  6. 31000000
  7. 8
  8. 1/4
  9. 4096
  10. 6561
  11. 1/512
  12. 1/10
  13. 0.052
  14. 7
  15. 0.00016
  16. 1/5
  17. 1/64
  18. 9
  19. 27
  20. 1/81
  21. 0.095
  22. 6400
  23. 49
  24. 1/100
  25. 25/4
  26. 4
  27. 3
  28. 1/7
  29. 6
  30. 24
  31. 3
  32. 1/25
  33. 2401
  34. 5/4
  35. 36
  36. 1/10
  37. 12
  38. 16
  39. 9
  40. 5

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