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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 254 · 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 7³? =
  2. 2.What is the value of 2⁻² (as a fraction)? =
  3. 3.What is the value of (8/9)⁻¹? =
  4. 4.Write (2²)³ as a single power 2ⁿ. What is n?
  5. 5.What is the value of 3² × 3⁻²? =
  6. 6.Write 4.1 × 10⁻² as a decimal. =
  7. 7.What is the value of (5/9)⁻²? =
  8. 8.What is the value of 8⁻³ (as a fraction)? =
  9. 9.What is the value of (2/3)⁻²? =
  10. 10.Write 4.7 × 10⁻² as a decimal. =
  11. 11.What is the value of 3² × 3⁻⁴? =
  12. 12.What is the value of 6²? =
  13. 13.What is the value of 2¹⁵? =
  14. 14.Write 5⁹ ÷ 5⁶ as a single power 5ⁿ. What is n?
  15. 15.Write (8⁶)⁷ as a single power 8ⁿ. What is n?
  16. 16.Write 7⁹ × 7⁷ as a single power 7ⁿ. What is n?
  17. 17.What is the value of 2¹²? =
  18. 18.Write 1.6 × 10⁻¹ as a decimal. =
  19. 19.Write 1.2 × 10⁻³ as a decimal. =
  20. 20.Write 6,20,000 in standard form as 6.2 × 10ⁿ. What is n?
  21. 21.Write (5³)⁹ as a single power 5ⁿ. What is n?
  22. 22.Write 6⁹ ÷ 6⁷ as a single power 6ⁿ. What is n?
  23. 23.Write 8.4 × 10⁻¹ as a decimal. =
  24. 24.What is the value of 7⁻³ (as a fraction)? =
  25. 25.Write 5¹⁵ ÷ 5⁹ as a single power 5ⁿ. What is n?
  26. 26.Write 9² × 9⁴ as a single power 9ⁿ. What is n?
  27. 27.Write 5.8 × 10⁻² as a decimal. =
  28. 28.What is the value of (6/7)⁻¹? =
  29. 29.Write 2.9 × 10⁻⁴ as a decimal. =
  30. 30.Write 3¹¹ ÷ 3² as a single power 3ⁿ. What is n?
  31. 31.Write 5.3 × 10⁻⁴ as a decimal. =
  32. 32.Write 4⁶ × 4⁵ as a single power 4ⁿ. What is n?
  33. 33.What is the value of 4³? =
  34. 34.Write 4,80,000 in standard form as 4.8 × 10ⁿ. What is n?
  35. 35.What is the value of 5⁻³ (as a fraction)? =
  36. 36.What is the value of 3¹ × 3⁻²? =
  37. 37.What is the value of 6⁴? =
  38. 38.What is the value of 8²? =
  39. 39.Write 8¹³ ÷ 8⁵ as a single power 8ⁿ. What is n?
  40. 40.What is the value of 3⁻³ (as a fraction)? =

Answer key

  1. 343
  2. 1/4
  3. 9/8
  4. 6
  5. 1
  6. 0.041
  7. 81/25
  8. 1/512
  9. 9/4
  10. 0.047
  11. 1/9
  12. 36
  13. 32768
  14. 3
  15. 42
  16. 16
  17. 4096
  18. 0.16
  19. 0.0012
  20. 5
  21. 27
  22. 2
  23. 0.84
  24. 1/343
  25. 6
  26. 6
  27. 0.058
  28. 7/6
  29. 0.00029
  30. 9
  31. 0.00053
  32. 11
  33. 64
  34. 5
  35. 1/125
  36. 1/3
  37. 1296
  38. 64
  39. 8
  40. 1/27

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