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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 577 · 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 9⁷ ÷ 9⁴ as a single power 9ⁿ. What is n?
  2. 2.What is the value of 2⁹? =
  3. 3.What is the value of 2³ × 2⁻⁵? =
  4. 4.Write 3⁶ × 3⁹ as a single power 3ⁿ. What is n?
  5. 5.What is the value of 10⁻³ (as a fraction)? =
  6. 6.What is the value of 2¹ × 2⁻¹? =
  7. 7.What is the value of 2¹⁴? =
  8. 8.What is the value of 5³ × 5⁻³? =
  9. 9.What is the value of 2⁷? =
  10. 10.Write 55,000 in standard form as 5.5 × 10ⁿ. What is n?
  11. 11.What is the value of 10² × 10⁻⁵? =
  12. 12.What is the value of 5²? =
  13. 13.What is the value of 4⁷? =
  14. 14.Write 5.8 × 10⁻³ as a decimal. =
  15. 15.What is the value of 2⁻⁸ (as a fraction)? =
  16. 16.Write 7¹³ ÷ 7⁶ as a single power 7ⁿ. What is n?
  17. 17.What is the value of 10¹ × 10⁻²? =
  18. 18.What is the value of 10²? =
  19. 19.Write 2⁹ × 2⁷ as a single power 2ⁿ. What is n?
  20. 20.What is the value of 10⁶ × 10⁻³? =
  21. 21.Write 6.5 × 10⁻¹ as a decimal. =
  22. 22.Write 6⁵ × 6³ as a single power 6ⁿ. What is n?
  23. 23.What is the value of 7⁻¹ (as a fraction)? =
  24. 24.What is the value of 4²? =
  25. 25.3.4 × 10³ =
  26. 26.What is the value of 2⁵ × 2⁻³? =
  27. 27.Write 63,000 in standard form as 6.3 × 10ⁿ. What is n?
  28. 28.What is the value of 10¹ × 10⁻¹? =
  29. 29.Write 5 × 10⁻⁴ as a decimal. =
  30. 30.What is the value of 10³ × 10⁻⁶? =
  31. 31.Write 5.3 × 10⁻² as a decimal. =
  32. 32.What is the value of 5⁴ × 5⁻⁶? =
  33. 33.What is the value of (5/6)⁻¹? =
  34. 34.Write 2,40,000 in standard form as 2.4 × 10ⁿ. What is n?
  35. 35.What is the value of (1/8)⁻²? =
  36. 36.What is the value of 5⁵ × 5⁻²? =
  37. 37.What is the value of 3³? =
  38. 38.Write 77,00,000 in standard form as 7.7 × 10ⁿ. What is n?
  39. 39.Write 3¹² ÷ 3⁷ as a single power 3ⁿ. What is n?
  40. 40.Write 3⁸ × 3² as a single power 3ⁿ. What is n?

Answer key

  1. 3
  2. 512
  3. 1/4
  4. 15
  5. 1/1000
  6. 1
  7. 16384
  8. 1
  9. 128
  10. 4
  11. 1/1000
  12. 25
  13. 16384
  14. 0.0058
  15. 1/256
  16. 7
  17. 1/10
  18. 100
  19. 16
  20. 1000
  21. 0.65
  22. 8
  23. 1/7
  24. 16
  25. 3400
  26. 4
  27. 4
  28. 1
  29. 0.0005
  30. 1/1000
  31. 0.053
  32. 1/25
  33. 6/5
  34. 5
  35. 64
  36. 125
  37. 27
  38. 6
  39. 5
  40. 10

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