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**Apply Properties of Rational Exponents**

Section 6.2 Apply Properties of Rational Exponents

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**Opener 6.2 1. Simplify : 2. Simplify: 3. True or False: 4. Simplify:**

6. Evaluate: 7. Evaluate: True False

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**= 73/4 = (61/2)2 (41/3)2 = 6(1/2 2) 4(1/3 2) EXAMPLE 1**

Use properties of exponents Use the properties of rational exponents to simplify the expression. a /4 71/2 = 7(1/4 + 1/2) = 73/4 b. (61/2 41/3)2 = (61/2)2 (41/3)2 = 6(1/2 2) 4(1/3 2) = /3 = 6 42/3 1 12 = c. (45 35)–1/5 = [(4 3)5]–1/5 = (125)–1/5 = 12[5 (–1/5)] = 12 –1 d. 5 51/3 51 51/3 = = 5(1 – 1/3) = 52/3 = 42 6 1/3 2 e. 421/ 61/3 = (71/3)2 = 7(1/3 2) = 72/3

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**Review of computing with fractions**

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Examples: Can’t combine they are not the same base: aman=am+n

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EXAMPLE 3 Use properties of radicals Use the properties of radicals to simplify the expression. a. 12 3 18 3 = 216 3 = = 6 Product property b. 80 4 5 80 5 4 = = 16 4 = 2 Quotient property

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Radical Examples!

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