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Rational Expon ents and Radicals

This article by Jeffrey Bivin explores the properties of rational exponents and radicals. It includes explanations, evaluations, and simplifications of various expressions. Learn how to express expressions using rational exponents and simplify them to their simplest radical form.

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Rational Expon ents and Radicals

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  1. Rational ExponentsandRadicals By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: December 11, 2007

  2. Properties of rational Exponents What can we say? Jeff Bivin -- LZHS

  3. Are these equivalent? YES YES YES YES Jeff Bivin -- LZHS

  4. Evaluate each Jeff Bivin -- LZHS

  5. Evaluate Jeff Bivin -- LZHS

  6. Now Consider remember Jeff Bivin -- LZHS

  7. Evaluate Jeff Bivin -- LZHS

  8. Consider Jeff Bivin -- LZHS

  9. One More or Jeff Bivin -- LZHS

  10. Evaluate Jeff Bivin -- LZHS

  11. Evaluate Let's make this easier! 5 goes into 14 how many times? How many left over? 5 goes into 26 how many times? How many left over? 5 goes into 33 how many times? How many left over? Jeff Bivin -- LZHS

  12. Evaluate 7 goes into the exponent 34 how many times? How many left over? 7 goes into the exponent 14 how many times? How many left over? 7 goes into the exponent 23 how many times? How many left over? Jeff Bivin -- LZHS

  13. Evaluate Don’t forget, even root – we need to use absolute value 4 goes into the exponent 15 how many times? How many left over? 4 goes into the exponent 18 how many times? How many left over? 4 goes into the exponent 29 how many times? How many left over? An even power can come out of the absolute value Jeff Bivin -- LZHS

  14. Evaluate: 3 goes into the power 4 how many times? How many left over? 3 goes into the power 2 how many times? How many left over? simplify Jeff Bivin -- LZHS

  15. Evaluate: 2 goes into the power 5 how many times? How many left over? 2 goes into the power 3 how many times? How many left over? simplify Jeff Bivin -- LZHS

  16. Evaluate: 2 goes into the power 7 how many times? How many left over? 2 goes into the power 2 how many times? How many left over? 2 goes into the power 9 how many times? How many left over? 2 goes into the power 27 how many times? How many left over? simplify Jeff Bivin -- LZHS

  17. Simplify Jeff Bivin -- LZHS

  18. Simplify Jeff Bivin -- LZHS

  19. Simplify Jeff Bivin -- LZHS

  20. Simplify Jeff Bivin -- LZHS

  21. Simplify Jeff Bivin -- LZHS

  22. Simplify Jeff Bivin -- LZHS Jeff Bivin -- LZHS

  23. Simplify Jeff Bivin -- LZHS

  24. Simplify Jeff Bivin -- LZHS

  25. Simplify Jeff Bivin -- LZHS

  26. Simplify Jeff Bivin -- LZHS

  27. Simplify Jeff Bivin -- LZHS

  28. Simplify Jeff Bivin -- LZHS

  29. Simplify Jeff Bivin -- LZHS

  30. Simplify Jeff Bivin -- LZHS

  31. Simplify Jeff Bivin -- LZHS

  32. Express using Rational Exponents Jeff Bivin -- LZHS

  33. Express using Rational Exponents Jeff Bivin -- LZHS

  34. Express using Rational Exponents Jeff Bivin -- LZHS

  35. Express in Simplest Radical From Jeff Bivin -- LZHS

  36. Express in Simplest Radical From Jeff Bivin -- LZHS

  37. Express in Simplest Radical From Jeff Bivin -- LZHS

  38. Express in Simplest Radical From Jeff Bivin -- LZHS

  39. Express in Simplest Radical From Jeff Bivin -- LZHS

  40. Express in Simplest Radical From 2 more reducing coming soon Jeff Bivin -- LZHS

  41. Express in Simplest Radical From Jeff Bivin -- LZHS

  42. Express in Simplest Radical From

  43. Express in Simplest Radical From

  44. Express in Simplest Radical From alternative

  45. Express in Simplest Radical From 2 Jeff Bivin -- LZHS

  46. Express in Simplest Radical From Jeff Bivin -- LZHS

  47. Express in Simplest Radical From Jeff Bivin -- LZHS

  48. Express in Simplest Radical From Jeff Bivin -- LZHS

  49. Express in Simplest Radical From more reducing coming now Jeff Bivin -- LZHS

  50. 1 Express in Simplest Radical From Jeff Bivin -- LZHS

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