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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 453 · 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 2,90,000 in standard form as 2.9 × 10ⁿ. What is n?
  2. 2.What is the value of 2⁶ × 2⁻⁶? =
  3. 3.What is the value of 5⁵ × 5⁻²? =
  4. 4.What is the value of 4⁶? =
  5. 5.What is the value of 3⁴ × 3⁻²? =
  6. 6.What is the value of 2² × 2⁻⁵? =
  7. 7.What is the value of 5⁴ × 5⁻¹? =
  8. 8.Write (2⁹)⁹ as a single power 2ⁿ. What is n?
  9. 9.Write 6³ × 6⁵ as a single power 6ⁿ. What is n?
  10. 10.What is the value of 9⁴? =
  11. 11.Write 56,00,000 in standard form as 5.6 × 10ⁿ. What is n?
  12. 12.Write 760 in standard form as 7.6 × 10ⁿ. What is n?
  13. 13.What is the value of 2¹⁵? =
  14. 14.Write 8.2 × 10⁻² as a decimal. =
  15. 15.What is the value of 6⁴? =
  16. 16.Write 3.6 × 10⁻³ as a decimal. =
  17. 17.Write 110 in standard form as 1.1 × 10ⁿ. What is n?
  18. 18.Write 4,10,00,000 in standard form as 4.1 × 10ⁿ. What is n?
  19. 19.Write 2 × 10⁻¹ as a decimal. =
  20. 20.What is the value of 3¹ × 3⁻¹? =
  21. 21.Write 9² × 9⁹ as a single power 9ⁿ. What is n?
  22. 22.What is the value of 6³? =
  23. 23.What is the value of 10¹ × 10⁻⁶? =
  24. 24.What is the value of 3⁵? =
  25. 25.What is the value of 10² × 10⁻¹? =
  26. 26.Write 12,000 in standard form as 1.2 × 10ⁿ. What is n?
  27. 27.Write 2,30,00,000 in standard form as 2.3 × 10ⁿ. What is n?
  28. 28.What is the value of 10⁶ × 10⁻¹? =
  29. 29.What is the value of 4⁷? =
  30. 30.What is the value of 5² × 5⁻⁶? =
  31. 31.What is the value of 9⁻¹ (as a fraction)? =
  32. 32.What is the value of 2¹ × 2⁻⁵? =
  33. 33.What is the value of 5⁵? =
  34. 34.Write (3⁵)³ as a single power 3ⁿ. What is n?
  35. 35.What is the value of 4⁵? =
  36. 36.6.3 × 10⁶ =
  37. 37.Write 6 × 10⁻² as a decimal. =
  38. 38.Write 3¹⁴ ÷ 3⁷ as a single power 3ⁿ. What is n?
  39. 39.What is the value of 2¹³? =
  40. 40.Write 2.4 × 10⁻² as a decimal. =

Answer key

  1. 5
  2. 1
  3. 125
  4. 4096
  5. 9
  6. 1/8
  7. 125
  8. 81
  9. 8
  10. 6561
  11. 6
  12. 2
  13. 32768
  14. 0.082
  15. 1296
  16. 0.0036
  17. 2
  18. 7
  19. 0.2
  20. 1
  21. 11
  22. 216
  23. 1/100000
  24. 243
  25. 10
  26. 4
  27. 7
  28. 100000
  29. 16384
  30. 1/625
  31. 1/9
  32. 1/16
  33. 3125
  34. 15
  35. 1024
  36. 6300000
  37. 0.06
  38. 7
  39. 8192
  40. 0.024

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