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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 146 · 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 5³ × 5⁻⁴? =
  2. 2.What is the value of 6³? =
  3. 3.What is the value of 2⁻⁵ (as a fraction)? =
  4. 4.What is the value of 9⁴? =
  5. 5.Write 2² × 2² as a single power 2ⁿ. What is n?
  6. 6.Write 9,70,00,000 in standard form as 9.7 × 10ⁿ. What is n?
  7. 7.Write 38,00,000 in standard form as 3.8 × 10ⁿ. What is n?
  8. 8.What is the value of 3¹⁰? =
  9. 9.Write 3.7 × 10⁻¹ as a decimal. =
  10. 10.What is the value of 10⁻¹ (as a fraction)? =
  11. 11.Write 1.7 × 10⁻⁴ as a decimal. =
  12. 12.Write 6,900 in standard form as 6.9 × 10ⁿ. What is n?
  13. 13.What is the value of 4⁻³ (as a fraction)? =
  14. 14.4.8 × 10² =
  15. 15.Write 30,000 in standard form as 3 × 10ⁿ. What is n?
  16. 16.Write 5¹⁵ ÷ 5⁷ as a single power 5ⁿ. What is n?
  17. 17.What is the value of 6⁻² (as a fraction)? =
  18. 18.Write 2.4 × 10⁻³ as a decimal. =
  19. 19.Write 5² × 5² as a single power 5ⁿ. What is n?
  20. 20.Write (4²)⁶ as a single power 4ⁿ. What is n?
  21. 21.Write 2,000 in standard form as 2 × 10ⁿ. What is n?
  22. 22.What is the value of 3¹ × 3⁻³? =
  23. 23.Write 34,000 in standard form as 3.4 × 10ⁿ. What is n?
  24. 24.Write (7²)² as a single power 7ⁿ. What is n?
  25. 25.Write 940 in standard form as 9.4 × 10ⁿ. What is n?
  26. 26.Write 6 × 10⁻² as a decimal. =
  27. 27.Write 5⁷ × 5⁹ as a single power 5ⁿ. What is n?
  28. 28.Write 6.4 × 10⁻³ as a decimal. =
  29. 29.9.2 × 10⁷ =
  30. 30.What is the value of 2⁻⁶ (as a fraction)? =
  31. 31.Write 3.6 × 10⁻² as a decimal. =
  32. 32.What is the value of 6²? =
  33. 33.What is the value of (2/5)⁻¹? =
  34. 34.Write 340 in standard form as 3.4 × 10ⁿ. What is n?
  35. 35.9.6 × 10⁷ =
  36. 36.Write (3⁴)⁷ as a single power 3ⁿ. What is n?
  37. 37.Write 92,00,000 in standard form as 9.2 × 10ⁿ. What is n?
  38. 38.Write 2.1 × 10⁻² as a decimal. =
  39. 39.What is the value of 2¹²? =
  40. 40.Write 6,40,00,000 in standard form as 6.4 × 10ⁿ. What is n?

Answer key

  1. 1/5
  2. 216
  3. 1/32
  4. 6561
  5. 4
  6. 7
  7. 6
  8. 59049
  9. 0.37
  10. 1/10
  11. 0.00017
  12. 3
  13. 1/64
  14. 480
  15. 4
  16. 8
  17. 1/36
  18. 0.0024
  19. 4
  20. 12
  21. 3
  22. 1/9
  23. 4
  24. 4
  25. 2
  26. 0.06
  27. 16
  28. 0.0064
  29. 92000000
  30. 1/64
  31. 0.036
  32. 36
  33. 5/2
  34. 2
  35. 96000000
  36. 28
  37. 6
  38. 0.021
  39. 4096
  40. 7

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