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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 758 · 40 sums
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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 49,000 in standard form as 4.9 × 10ⁿ. What is n?
  2. 2.Write 92,00,000 in standard form as 9.2 × 10ⁿ. What is n?
  3. 3.What is the value of 2¹⁶? =
  4. 4.What is the value of 2⁻⁸ (as a fraction)? =
  5. 5.What is the value of 3² × 3⁻⁶? =
  6. 6.What is the value of 2²? =
  7. 7.What is the value of 6⁴? =
  8. 8.Write (5⁹)⁵ as a single power 5ⁿ. What is n?
  9. 9.Write 1.6 × 10⁻³ as a decimal. =
  10. 10.What is the value of 10² × 10⁻¹? =
  11. 11.Write 3¹³ ÷ 3⁹ as a single power 3ⁿ. What is n?
  12. 12.What is the value of 2⁴? =
  13. 13.Write 3.5 × 10⁻¹ as a decimal. =
  14. 14.Write 7⁵ × 7² as a single power 7ⁿ. What is n?
  15. 15.What is the value of (4/7)⁻²? =
  16. 16.What is the value of 8⁵? =
  17. 17.Write 8² × 8⁵ as a single power 8ⁿ. What is n?
  18. 18.What is the value of 2⁶ × 2⁻⁵? =
  19. 19.What is the value of 4⁷? =
  20. 20.Write 2⁸ × 2² as a single power 2ⁿ. What is n?
  21. 21.Write 6¹¹ ÷ 6⁸ as a single power 6ⁿ. What is n?
  22. 22.Write 2,600 in standard form as 2.6 × 10ⁿ. What is n?
  23. 23.What is the value of 7⁵? =
  24. 24.Write (4⁵)⁸ as a single power 4ⁿ. What is n?
  25. 25.What is the value of (5/8)⁻¹? =
  26. 26.Write 9,800 in standard form as 9.8 × 10ⁿ. What is n?
  27. 27.What is the value of 2⁻⁶ (as a fraction)? =
  28. 28.Write 5.1 × 10⁻⁴ as a decimal. =
  29. 29.4.2 × 10³ =
  30. 30.What is the value of 5¹ × 5⁻³? =
  31. 31.Write 3¹⁵ ÷ 3⁷ as a single power 3ⁿ. What is n?
  32. 32.Write 85,000 in standard form as 8.5 × 10ⁿ. What is n?
  33. 33.What is the value of 10⁴ × 10⁻⁶? =
  34. 34.What is the value of 2¹²? =
  35. 35.Write (5²)² as a single power 5ⁿ. What is n?
  36. 36.Write 7¹⁶ ÷ 7⁸ as a single power 7ⁿ. What is n?
  37. 37.What is the value of 3⁻⁶ (as a fraction)? =
  38. 38.What is the value of 2⁻⁴ (as a fraction)? =
  39. 39.What is the value of (1/2)⁻¹? =
  40. 40.Write (2⁸)⁴ as a single power 2ⁿ. What is n?

Answer key

  1. 4
  2. 6
  3. 65536
  4. 1/256
  5. 1/81
  6. 4
  7. 1296
  8. 45
  9. 0.0016
  10. 10
  11. 4
  12. 16
  13. 0.35
  14. 7
  15. 49/16
  16. 32768
  17. 7
  18. 2
  19. 16384
  20. 10
  21. 3
  22. 3
  23. 16807
  24. 40
  25. 8/5
  26. 3
  27. 1/64
  28. 0.00051
  29. 4200
  30. 1/25
  31. 8
  32. 4
  33. 1/100
  34. 4096
  35. 4
  36. 8
  37. 1/729
  38. 1/16
  39. 2
  40. 32

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