1. Rational Exponents and Radicals
By: Jeffrey Bivin
Lake Zurich High School
Last Updated: December 11, 2007

2. Properties of rational Exponents
What can we say?
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3. Are these equivalent?
YES
YES
YES
YES
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4. Evaluate each
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5. Evaluate
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6. Now Consider
remember
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7. Evaluate
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8. Consider
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9. One More or
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10. Evaluate
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11. Evaluate Let's make this easier! Jeff Bivin -- LZHS
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?
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12. Evaluate Jeff Bivin -- LZHS
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?
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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
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14. Evaluate: simplify Jeff Bivin -- LZHS
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
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15. Evaluate: simplify Jeff Bivin -- LZHS
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
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16. Evaluate: simplify Jeff Bivin -- LZHS
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
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17. Simplify
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18. Simplify
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19. Simplify
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20. Simplify
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21. Simplify
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22. Simplify
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23. Simplify
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24. Simplify
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25. Simplify
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26. Simplify
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27. Simplify
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28. Simplify
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29. Simplify
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30. Simplify
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31. Simplify
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32. Express using Rational Exponents
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33. Express using Rational Exponents
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34. Express using Rational Exponents
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35. Express in Simplest Radical From
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36. Express in Simplest Radical From
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37. Express in Simplest Radical From
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38. Express in Simplest Radical From
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39. Express in Simplest Radical From
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40. Express in Simplest Radical From2
more reducing
coming soon
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41. Express in Simplest Radical From
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42. Express in Simplest Radical From

43. Express in Simplest Radical From

44. Express in Simplest Radical From
alternative

45. Express in Simplest Radical From2
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46. Express in Simplest Radical From
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47. Express in Simplest Radical From
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48. Express in Simplest Radical From
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49. Express in Simplest Radical From
more reducing
coming now
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50. Express in Simplest Radical From1
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51. Express in Simplest Radical From1
remember
16 = 24
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52. Simplify
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53. Simplify
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54. Simplify
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55. Simplify
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