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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 16 · 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 3⁷? =
  2. 2.What is the value of 2¹³? =
  3. 3.2.2 × 10⁶ =
  4. 4.Write 7³ × 7⁴ as a single power 7ⁿ. What is n?
  5. 5.What is the value of 3⁻³ (as a fraction)? =
  6. 6.Write 3¹⁵ ÷ 3⁹ as a single power 3ⁿ. What is n?
  7. 7.Write (2⁷)⁵ as a single power 2ⁿ. What is n?
  8. 8.6.4 × 10³ =
  9. 9.What is the value of 3⁴ × 3⁻⁵? =
  10. 10.Write (9⁷)⁹ as a single power 9ⁿ. What is n?
  11. 11.What is the value of 2¹⁰? =
  12. 12.What is the value of (5/7)⁻¹? =
  13. 13.Write 1,700 in standard form as 1.7 × 10ⁿ. What is n?
  14. 14.What is the value of (3/8)⁻¹? =
  15. 15.Write 6.8 × 10⁻¹ as a decimal. =
  16. 16.Write 8⁵ ÷ 8³ as a single power 8ⁿ. What is n?
  17. 17.Write 2¹⁴ ÷ 2⁶ as a single power 2ⁿ. What is n?
  18. 18.Write 7⁵ × 7⁵ as a single power 7ⁿ. What is n?
  19. 19.What is the value of (4/5)⁻¹? =
  20. 20.What is the value of 3²? =
  21. 21.What is the value of 2² × 2⁻³? =
  22. 22.Write (3⁸)⁸ as a single power 3ⁿ. What is n?
  23. 23.What is the value of (1/7)⁻²? =
  24. 24.What is the value of 3¹ × 3⁻¹? =
  25. 25.3.3 × 10² =
  26. 26.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  27. 27.What is the value of 3⁴ × 3⁻¹? =
  28. 28.What is the value of 2⁴? =
  29. 29.What is the value of 2⁻⁶ (as a fraction)? =
  30. 30.Write 6.3 × 10⁻² as a decimal. =
  31. 31.Write 5.9 × 10⁻⁴ as a decimal. =
  32. 32.Write (3⁷)⁶ as a single power 3ⁿ. What is n?
  33. 33.Write 75,000 in standard form as 7.5 × 10ⁿ. What is n?
  34. 34.What is the value of 3⁵? =
  35. 35.Write 8³ × 8² as a single power 8ⁿ. What is n?
  36. 36.What is the value of 10¹ × 10⁻²? =
  37. 37.What is the value of 4⁻⁴ (as a fraction)? =
  38. 38.What is the value of 3¹ × 3⁻⁵? =
  39. 39.What is the value of 7⁴? =
  40. 40.3.2 × 10³ =

Answer key

  1. 2187
  2. 8192
  3. 2200000
  4. 7
  5. 1/27
  6. 6
  7. 35
  8. 6400
  9. 1/3
  10. 63
  11. 1024
  12. 7/5
  13. 3
  14. 8/3
  15. 0.68
  16. 2
  17. 8
  18. 10
  19. 5/4
  20. 9
  21. 1/2
  22. 64
  23. 49
  24. 1
  25. 330
  26. 9
  27. 27
  28. 16
  29. 1/64
  30. 0.063
  31. 0.00059
  32. 42
  33. 4
  34. 243
  35. 5
  36. 1/10
  37. 1/256
  38. 1/81
  39. 2401
  40. 3200

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