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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 511 · 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.Write 5¹⁷ ÷ 5⁸ as a single power 5ⁿ. What is n?
  2. 2.2.7 × 10⁴ =
  3. 3.Write 4.4 × 10⁻¹ as a decimal. =
  4. 4.What is the value of 2¹⁵? =
  5. 5.Write 6,800 in standard form as 6.8 × 10ⁿ. What is n?
  6. 6.Write 9.4 × 10⁻² as a decimal. =
  7. 7.7.9 × 10² =
  8. 8.Write 4.9 × 10⁻² as a decimal. =
  9. 9.Write 8³ × 8³ as a single power 8ⁿ. What is n?
  10. 10.What is the value of 5⁴ × 5⁻²? =
  11. 11.Write (3⁷)⁶ as a single power 3ⁿ. What is n?
  12. 12.What is the value of 5⁴ × 5⁻³? =
  13. 13.What is the value of 3⁴? =
  14. 14.What is the value of 10⁶ × 10⁻⁶? =
  15. 15.3.2 × 10⁴ =
  16. 16.What is the value of (2/3)⁻¹? =
  17. 17.Write 3⁹ ÷ 3⁶ as a single power 3ⁿ. What is n?
  18. 18.What is the value of 7⁻¹ (as a fraction)? =
  19. 19.What is the value of 5⁻¹ (as a fraction)? =
  20. 20.What is the value of 2⁻⁶ (as a fraction)? =
  21. 21.Write 9⁹ × 9⁵ as a single power 9ⁿ. What is n?
  22. 22.What is the value of (1/3)⁻¹? =
  23. 23.What is the value of 2¹²? =
  24. 24.What is the value of (6/7)⁻¹? =
  25. 25.Write (5⁹)⁴ as a single power 5ⁿ. What is n?
  26. 26.What is the value of (5/7)⁻²? =
  27. 27.Write 7,10,00,000 in standard form as 7.1 × 10ⁿ. What is n?
  28. 28.Write 3² × 3⁴ as a single power 3ⁿ. What is n?
  29. 29.Write 2,70,000 in standard form as 2.7 × 10ⁿ. What is n?
  30. 30.6.1 × 10² =
  31. 31.Write 7.5 × 10⁻² as a decimal. =
  32. 32.What is the value of 5⁵ × 5⁻³? =
  33. 33.What is the value of 7⁻³ (as a fraction)? =
  34. 34.What is the value of 10⁵ × 10⁻⁴? =
  35. 35.What is the value of 4⁻⁴ (as a fraction)? =
  36. 36.What is the value of 3³ × 3⁻⁵? =
  37. 37.What is the value of 2⁵ × 2⁻⁴? =
  38. 38.Write (2⁹)⁷ as a single power 2ⁿ. What is n?
  39. 39.What is the value of 2⁻³ (as a fraction)? =
  40. 40.What is the value of 5⁷? =

Answer key

  1. 9
  2. 27000
  3. 0.44
  4. 32768
  5. 3
  6. 0.094
  7. 790
  8. 0.049
  9. 6
  10. 25
  11. 42
  12. 5
  13. 81
  14. 1
  15. 32000
  16. 3/2
  17. 3
  18. 1/7
  19. 1/5
  20. 1/64
  21. 14
  22. 3
  23. 4096
  24. 7/6
  25. 36
  26. 49/25
  27. 7
  28. 6
  29. 5
  30. 610
  31. 0.075
  32. 25
  33. 1/343
  34. 10
  35. 1/256
  36. 1/9
  37. 2
  38. 63
  39. 1/8
  40. 78125

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