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Class 8 Maths Worksheet: Exponents and Powers

Maths worksheets lesson 57: Exponents and powers · Set 693 · 40 sums
TalentJR

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 8¹⁵ ÷ 8⁸ as a single power 8ⁿ. What is n?
  2. 2.What is the value of 2⁻³ (as a fraction)? =
  3. 3.Write 9.3 × 10⁻⁴ as a decimal. =
  4. 4.What is the value of 9⁻¹ (as a fraction)? =
  5. 5.Write 9¹¹ ÷ 9⁵ as a single power 9ⁿ. What is n?
  6. 6.Write 5 × 10⁻¹ as a decimal. =
  7. 7.Write (9⁹)⁷ as a single power 9ⁿ. What is n?
  8. 8.What is the value of 2¹⁰? =
  9. 9.Write 8⁶ × 8⁶ as a single power 8ⁿ. What is n?
  10. 10.Write 8.4 × 10⁻¹ as a decimal. =
  11. 11.Write 850 in standard form as 8.5 × 10ⁿ. What is n?
  12. 12.What is the value of (5/9)⁻¹? =
  13. 13.What is the value of 4⁻³ (as a fraction)? =
  14. 14.What is the value of (8/9)⁻²? =
  15. 15.What is the value of 5⁷? =
  16. 16.What is the value of 3⁵ × 3⁻⁵? =
  17. 17.Write 4² × 4⁸ as a single power 4ⁿ. What is n?
  18. 18.Write 690 in standard form as 6.9 × 10ⁿ. What is n?
  19. 19.What is the value of (1/6)⁻²? =
  20. 20.What is the value of 10¹ × 10⁻⁴? =
  21. 21.Write 7¹¹ ÷ 7⁸ as a single power 7ⁿ. What is n?
  22. 22.What is the value of 5² × 5⁻⁴? =
  23. 23.What is the value of 2⁻² (as a fraction)? =
  24. 24.Write 7,50,00,000 in standard form as 7.5 × 10ⁿ. What is n?
  25. 25.What is the value of 5³ × 5⁻⁶? =
  26. 26.What is the value of 10³? =
  27. 27.What is the value of 5⁴ × 5⁻¹? =
  28. 28.What is the value of 5³? =
  29. 29.What is the value of 7²? =
  30. 30.Write 420 in standard form as 4.2 × 10ⁿ. What is n?
  31. 31.5.8 × 10² =
  32. 32.5.2 × 10⁶ =
  33. 33.Write 4.7 × 10⁻² as a decimal. =
  34. 34.What is the value of 7⁻³ (as a fraction)? =
  35. 35.Write 310 in standard form as 3.1 × 10ⁿ. What is n?
  36. 36.Write 1.7 × 10⁻² as a decimal. =
  37. 37.Write (4⁵)⁴ as a single power 4ⁿ. What is n?
  38. 38.Write 1.5 × 10⁻² as a decimal. =
  39. 39.Write 7⁵ × 7⁶ as a single power 7ⁿ. What is n?
  40. 40.Write (7⁸)² as a single power 7ⁿ. What is n?

Answer key

  1. 7
  2. 1/8
  3. 0.00093
  4. 1/9
  5. 6
  6. 0.5
  7. 63
  8. 1024
  9. 12
  10. 0.84
  11. 2
  12. 9/5
  13. 1/64
  14. 81/64
  15. 78125
  16. 1
  17. 10
  18. 2
  19. 36
  20. 1/1000
  21. 3
  22. 1/25
  23. 1/4
  24. 7
  25. 1/125
  26. 1000
  27. 125
  28. 125
  29. 49
  30. 2
  31. 580
  32. 5200000
  33. 0.047
  34. 1/343
  35. 2
  36. 0.017
  37. 20
  38. 0.015
  39. 11
  40. 16

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