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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 581 · 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 7¹¹ ÷ 7⁶ as a single power 7ⁿ. What is n?
  2. 2.Write (4⁴)⁹ as a single power 4ⁿ. What is n?
  3. 3.Write 1.4 × 10⁻³ as a decimal. =
  4. 4.What is the value of 2³? =
  5. 5.What is the value of (3/8)⁻¹? =
  6. 6.Write 5.2 × 10⁻² as a decimal. =
  7. 7.Write 8.5 × 10⁻⁴ as a decimal. =
  8. 8.Write 5⁴ × 5⁵ as a single power 5ⁿ. What is n?
  9. 9.Write 560 in standard form as 5.6 × 10ⁿ. What is n?
  10. 10.Write (4⁵)⁴ as a single power 4ⁿ. What is n?
  11. 11.What is the value of (4/7)⁻¹? =
  12. 12.What is the value of (2/5)⁻²? =
  13. 13.1.6 × 10⁵ =
  14. 14.What is the value of 2³ × 2⁻²? =
  15. 15.Write 63,000 in standard form as 6.3 × 10ⁿ. What is n?
  16. 16.What is the value of 2¹⁴? =
  17. 17.What is the value of 6³? =
  18. 18.What is the value of 6⁵? =
  19. 19.What is the value of 5³ × 5⁻¹? =
  20. 20.Write (7⁶)⁶ as a single power 7ⁿ. What is n?
  21. 21.Write 3¹³ ÷ 3⁸ as a single power 3ⁿ. What is n?
  22. 22.Write 2.3 × 10⁻³ as a decimal. =
  23. 23.What is the value of 3¹⁰? =
  24. 24.What is the value of 6⁴? =
  25. 25.Write 1.2 × 10⁻³ as a decimal. =
  26. 26.Write 5¹³ ÷ 5⁶ as a single power 5ⁿ. What is n?
  27. 27.Write 2.7 × 10⁻⁴ as a decimal. =
  28. 28.What is the value of 6⁻³ (as a fraction)? =
  29. 29.What is the value of (3/4)⁻¹? =
  30. 30.Write 7⁴ × 7⁴ as a single power 7ⁿ. What is n?
  31. 31.Write (2⁶)³ as a single power 2ⁿ. What is n?
  32. 32.Write 71,000 in standard form as 7.1 × 10ⁿ. What is n?
  33. 33.What is the value of (1/8)⁻²? =
  34. 34.What is the value of 9⁻² (as a fraction)? =
  35. 35.What is the value of 10⁴? =
  36. 36.Write 1,20,000 in standard form as 1.2 × 10ⁿ. What is n?
  37. 37.What is the value of 2⁴ × 2⁻⁴? =
  38. 38.What is the value of 2⁵ × 2⁻⁶? =
  39. 39.What is the value of 8⁻¹ (as a fraction)? =
  40. 40.Write (9⁵)⁶ as a single power 9ⁿ. What is n?

Answer key

  1. 5
  2. 36
  3. 0.0014
  4. 8
  5. 8/3
  6. 0.052
  7. 0.00085
  8. 9
  9. 2
  10. 20
  11. 7/4
  12. 25/4
  13. 160000
  14. 2
  15. 4
  16. 16384
  17. 216
  18. 7776
  19. 25
  20. 36
  21. 5
  22. 0.0023
  23. 59049
  24. 1296
  25. 0.0012
  26. 7
  27. 0.00027
  28. 1/216
  29. 4/3
  30. 8
  31. 18
  32. 4
  33. 64
  34. 1/81
  35. 10000
  36. 5
  37. 1
  38. 1/2
  39. 1/8
  40. 30

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