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10.2 Rational Exponents

10.2 Rational Exponents. Objective 1. Use exponential notation for n th roots. Slide 10.2- 2. Use exponential notation for n th roots. Notice that the denominator of the rational exponent is the index of the radical. Slide 10.2- 3. CLASSROOM EXAMPLE 1.

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10.2 Rational Exponents

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  1. 10.2 Rational Exponents

  2. Objective 1 Use exponential notation for nth roots. Slide 10.2- 2

  3. Use exponential notation for nth roots. Notice that the denominator of the rational exponent is the index of the radical. Slide 10.2- 3

  4. CLASSROOM EXAMPLE 1 Evaluating Exponentials of the Form a1/n Solution: Evaluate each exponential. Is not a real number because the radicand, – 81, is negative and the index, 4, is even. Slide 10.2- 4

  5. Objective 2 Define and use expressions of the form am/n. Slide 10.2- 5

  6. Define and use expressions of the form am/n. Slide 10.2- 6

  7. CLASSROOM EXAMPLE 2 Evaluating Exponentials of the Form am/n Solution: Evaluate each exponential. is not a real number, since or is not a real number. Slide 10.2- 7

  8. A negative exponent does not necessarily lead to a negative result. Negative exponents lead to reciprocals, which may be positive. Define and use expressions of the form am/n. Slide 10.2- 8

  9. CLASSROOM EXAMPLE 3 Evaluating Exponentials with Negative Rational Exponents Solution: Evaluate each exponential. Slide 10.2- 9

  10. Define and use expressions of the form am/n. Slide 10.2- 10

  11. Define and use expressions of the form am/n. Slide 10.2- 11

  12. Objective 3 Convert between radicals and rational exponents. Slide 10.2- 12

  13. CLASSROOM EXAMPLE 4 Converting between Rational Exponents and Radicals Solution: Write each exponential as a radical. Assume that all variables, represent positive real numbers. Slide 10.2- 13

  14. CLASSROOM EXAMPLE 4 Converting between Rational Exponents and Radicals (cont’d) Write each radical as an exponential. Solution: = |z| Slide 10.2- 14

  15. Objective 4 Use the rules for exponents with rational exponents. Slide 10.2- 15

  16. Use the rules for exponents with rational exponents. Slide 10.2- 16

  17. CLASSROOM EXAMPLE 5 Applying Rules for Rational Exponents Write with only positive exponents. Assume that all variables represent positive real numbers. Solution: Slide 10.2- 17

  18. CLASSROOM EXAMPLE 5 Applying Rules for Rational Exponents (cont’d) Write with only positive exponents. Assume that all variables represent positive real numbers. Solution: Slide 10.2- 18

  19. CLASSROOM EXAMPLE 6 Applying Rules for Rational Exponents Write all radicals as exponentials, and then apply the rules for rational exponents. Leave answers in exponential form. Assume that all variables represent positive real numbers. Solution: Slide 10.2- 19

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