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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 245 · 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.What is the value of 5²? =
  2. 2.Write 1.2 × 10⁻¹ as a decimal. =
  3. 3.Write 64,000 in standard form as 6.4 × 10ⁿ. What is n?
  4. 4.Write 7⁹ × 7² as a single power 7ⁿ. What is n?
  5. 5.What is the value of 2³ × 2⁻⁶? =
  6. 6.Write 4.3 × 10⁻¹ as a decimal. =
  7. 7.Write 5¹¹ ÷ 5⁴ as a single power 5ⁿ. What is n?
  8. 8.Write (2³)⁶ as a single power 2ⁿ. What is n?
  9. 9.What is the value of 3² × 3⁻¹? =
  10. 10.Write 3⁷ × 3⁹ as a single power 3ⁿ. What is n?
  11. 11.Write 8,30,000 in standard form as 8.3 × 10ⁿ. What is n?
  12. 12.What is the value of 10³ × 10⁻⁵? =
  13. 13.1.7 × 10³ =
  14. 14.What is the value of 8⁴? =
  15. 15.What is the value of 5⁴ × 5⁻³? =
  16. 16.Write 4⁴ × 4⁸ as a single power 4ⁿ. What is n?
  17. 17.What is the value of (2/3)⁻¹? =
  18. 18.What is the value of 6⁻¹ (as a fraction)? =
  19. 19.2.8 × 10⁴ =
  20. 20.What is the value of (1/4)⁻¹? =
  21. 21.What is the value of 5⁶ × 5⁻¹? =
  22. 22.Write 3⁴ × 3⁸ as a single power 3ⁿ. What is n?
  23. 23.What is the value of 4⁵? =
  24. 24.What is the value of 5⁴ × 5⁻⁶? =
  25. 25.Write 6¹⁷ ÷ 6⁸ as a single power 6ⁿ. What is n?
  26. 26.Write 2.8 × 10⁻¹ as a decimal. =
  27. 27.Write (3⁹)³ as a single power 3ⁿ. What is n?
  28. 28.Write 8.8 × 10⁻¹ as a decimal. =
  29. 29.What is the value of 2¹³? =
  30. 30.Write 9³ × 9⁴ as a single power 9ⁿ. What is n?
  31. 31.What is the value of 5⁶? =
  32. 32.4.6 × 10⁴ =
  33. 33.8.2 × 10⁴ =
  34. 34.Write 50,00,000 in standard form as 5 × 10ⁿ. What is n?
  35. 35.What is the value of 10⁵? =
  36. 36.What is the value of 5⁶ × 5⁻²? =
  37. 37.Write 1.9 × 10⁻² as a decimal. =
  38. 38.Write 8.2 × 10⁻¹ as a decimal. =
  39. 39.What is the value of (1/3)⁻¹? =
  40. 40.Write 3⁸ ÷ 3⁶ as a single power 3ⁿ. What is n?

Answer key

  1. 25
  2. 0.12
  3. 4
  4. 11
  5. 1/8
  6. 0.43
  7. 7
  8. 18
  9. 3
  10. 16
  11. 5
  12. 1/100
  13. 1700
  14. 4096
  15. 5
  16. 12
  17. 3/2
  18. 1/6
  19. 28000
  20. 4
  21. 3125
  22. 12
  23. 1024
  24. 1/25
  25. 9
  26. 0.28
  27. 27
  28. 0.88
  29. 8192
  30. 7
  31. 15625
  32. 46000
  33. 82000
  34. 6
  35. 100000
  36. 625
  37. 0.019
  38. 0.82
  39. 3
  40. 2

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