Rational Exponents and Nth Roots

Learn about rational exponents, nth roots, even and odd exponents, evaluating expressions, rules for rational exponents, simplifying radicals, and more in this informative content with visual examples.

• Rational Exponents
• Nth Roots
• Simplifying Radicals
• Evaluating Expressions
• Math Concepts

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Uploaded on Apr 19, 2024 | 1 Views

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Presentation Transcript

1. How Do We Use Rational Exponents? Do Now: Perform the indicated operation and simplify 1. 2. 1

2. nth Roots nth Roots An nth root of number a is a number whose nth power is a. a number whose nth power is a = na If the index n is even, then the radicand a must be nonnegative. is not a real number 5 32 2 = = 4 4 16 2, 16 but 2

3. Square Root of x2 x = 2 x 3 Page 393

4. Radicals 4

5. Rational Exponents 5

6. Exponent 1/n When n Is Even 6

7. When n Is Even 1 = = 100 100 10 2 1 = = 4 625 625 5 4 1 = = 6 64 64 2 6 1 ( ) = 4 4 is not yet defined 2 7

8. Exponent 1/n When n Is Odd 8

9. Exponent 1/n When n Is Odd 1 = = 3 27 27 3 3 1 ( ) = = 3 27 27 3 3 1 1 1 1 5 = = 5 32 32 2 9

10. nth Root of Zero 0 = n 0 10

11. Rational Exponents 11

12. Evaluating in Either Order ( ) 8 2 ( ) 8 or ( ) 2 2 2 = = = 3 4 3 2 ( ) 8 = = = 2 3 3 8 64 4 3 12

13. Negative Rational Exponents 13

14. Evaluating a-m/n 1 1 1 1 2 ( ) 8 = = = = ( ) 8 3 ( ) 2 2 2 2 4 ( ) 8 3 3 14

15. Rules for Rational Exponents 15 7-6

16. Simplifying ( ) a 1 = = 6 6 y y y 6 6 1 1 ( )= ab b 3 2 16

17. Simplifying ( ) y 1 = = 6 6 y y 6 6 1 1 1 1 ( ) ( ) = 1 1 a b ab a b a b 3 3 2 2 1 1 + + 1 1 = a b 3 2 2 3 = a b 3 2 17

18. Simplifying ( ) a 1 = = 6 6 y y y 6 6 1 2 1 3 ( ) = b ab a b 3 3 2 2 ( ) = 1 8 10 12 9 x y z 2 18

19. Multiplying Radicals Different Indices 1 1 1 1 3 + = = = = = 3 4 4 4 2 2 2 2 2 2 2 8 4 2 4 2 4 = 3 2 3 19

20. Multiplying Radicals Different Indices 1 1 1 1 3 + = = = = = 3 4 4 4 2 2 2 2 2 2 2 8 4 2 4 2 4 1 1 = = 3 2 3 2 3 3 2 20

21. Different Indices 1 1 1 1 3 + = = = = = 3 4 4 4 2 2 2 2 2 2 2 8 4 2 4 2 4 1 2 3 1 = = = 3 2 3 2 3 2 3 3 6 6 2 21

22. Different Indices 1 1 1 1 3 + = = = = = 3 4 4 4 2 2 2 2 2 2 2 8 4 2 4 2 4 1 2 3 1 = = = = 6 2 3 6 3 2 3 2 3 2 3 2 3 3 6 6 2 22

23. Different Indices 1 1 1 1 3 + = = = = = 3 4 4 4 2 2 2 2 2 2 2 8 4 2 4 2 4 1 2 3 1 = = = = 6 2 3 6 3 6 2 3 2 3 2 3 2 3 108 3 6 6 2 23

24. Rational Exponents Eliminate the root, then the power 2 = 2 a 3 24

25. Eliminate the Root, Then the Power 2 = 2 a 3 3 2 = 3 2 a 3 = 2 8 a = 2 8 a = 2 2 a CHECK 25

26. Negative Exponents 2 ( ) = 1 1 r 3 26

27. Negative Exponents Eliminate the root, then the power ( ) r 1 = 2 1 3 3 2 ( ) = 3 1 1 r 3 ( ) 2 = 1 1 r ( ) 2 = 1 1 r = 1 1 r = = 2 0 r r 27 CHECK

28. Negative Exponents Eliminate the root, then the power 2 ( ) = 2 3 1 t 3 28

29. No Solution Eliminate the root, then the power 2 ( ) = 2 3 1 t 3 3 2 ( ) ( ) 3 = 2 3 1 t 3 ( ) 2 = 2 3 1 t ( ) 2 = 2 3 1 t 29

30. No Solution Eliminate the root, then the power 2 ( ) = 2 3 1 t 3 3 2 ( ) ( ) 3 = 2 3 1 t 3 ( ) 2 = 2 3 1 t ( ) 2 = 2 3 1 t No real solution 30

31. Strategy for Solving Equations with Exponents and Radicals 31

32. This powerpoint was kindly donated to www.worldofteaching.com http://www.worldofteaching.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching. 32