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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 217 · 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 36,00,000 in standard form as 3.6 × 10ⁿ. What is n?
  2. 2.What is the value of (3/5)⁻²? =
  3. 3.Write (3⁶)³ as a single power 3ⁿ. What is n?
  4. 4.What is the value of 5² × 5⁻¹? =
  5. 5.Write 51,000 in standard form as 5.1 × 10ⁿ. What is n?
  6. 6.Write 6,100 in standard form as 6.1 × 10ⁿ. What is n?
  7. 7.What is the value of 3⁻¹ (as a fraction)? =
  8. 8.What is the value of 9⁵? =
  9. 9.Write 8,500 in standard form as 8.5 × 10ⁿ. What is n?
  10. 10.Write 1.5 × 10⁻² as a decimal. =
  11. 11.Write 9 × 10⁻² as a decimal. =
  12. 12.3.1 × 10² =
  13. 13.What is the value of 4⁻² (as a fraction)? =
  14. 14.Write 53,00,000 in standard form as 5.3 × 10ⁿ. What is n?
  15. 15.What is the value of 2⁻⁵ (as a fraction)? =
  16. 16.4.8 × 10⁶ =
  17. 17.What is the value of 5²? =
  18. 18.What is the value of 8⁻³ (as a fraction)? =
  19. 19.Write 2⁹ × 2⁵ as a single power 2ⁿ. What is n?
  20. 20.Write 5² × 5⁹ as a single power 5ⁿ. What is n?
  21. 21.What is the value of (4/7)⁻¹? =
  22. 22.What is the value of (1/6)⁻²? =
  23. 23.Write 4¹² ÷ 4⁵ as a single power 4ⁿ. What is n?
  24. 24.What is the value of (1/6)⁻¹? =
  25. 25.What is the value of 10³ × 10⁻⁴? =
  26. 26.Write 79,000 in standard form as 7.9 × 10ⁿ. What is n?
  27. 27.Write 3.7 × 10⁻⁴ as a decimal. =
  28. 28.What is the value of 2³? =
  29. 29.Write (7⁹)³ as a single power 7ⁿ. What is n?
  30. 30.What is the value of (6/7)⁻¹? =
  31. 31.Write 3¹⁴ ÷ 3⁹ as a single power 3ⁿ. What is n?
  32. 32.Write 7⁴ × 7⁹ as a single power 7ⁿ. What is n?
  33. 33.What is the value of 5⁷? =
  34. 34.What is the value of 5⁻² (as a fraction)? =
  35. 35.What is the value of 3⁵ × 3⁻⁶? =
  36. 36.What is the value of 5³ × 5⁻²? =
  37. 37.What is the value of (1/7)⁻¹? =
  38. 38.What is the value of 5⁵ × 5⁻³? =
  39. 39.What is the value of 10⁴ × 10⁻²? =
  40. 40.What is the value of 10² × 10⁻⁶? =

Answer key

  1. 6
  2. 25/9
  3. 18
  4. 5
  5. 4
  6. 3
  7. 1/3
  8. 59049
  9. 3
  10. 0.015
  11. 0.09
  12. 310
  13. 1/16
  14. 6
  15. 1/32
  16. 4800000
  17. 25
  18. 1/512
  19. 14
  20. 11
  21. 7/4
  22. 36
  23. 7
  24. 6
  25. 1/10
  26. 4
  27. 0.00037
  28. 8
  29. 27
  30. 7/6
  31. 5
  32. 13
  33. 78125
  34. 1/25
  35. 1/3
  36. 5
  37. 7
  38. 25
  39. 100
  40. 1/10000

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