Algebra 2 7.2 Notes - 7.2 Properties of Rational Exponents...

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Properties of Rational Exponents Goals p Use properties of rational exponents. p Use properties of rational exponents in real life. 7.2 VOCABULARY Simplest form of a radical A radical expression after you apply the properties of radicals, remove any perfect n th powers, and rationalize any denominators Like radicals Two radical expressions that have the same index and the same radicand Your Notes PROPERTIES OF RATIONAL EXPONENTS Let a and b be real numbers and let m and n be rational numbers. The following properties have the same names as those listed in Lesson 6.1, but now apply to rational exponents as illustrated. Property Example 1. a m p a n ± a m ² n 3 1/2 p 3 3/2 ± 3 (1/2 ² 3/2) ± 3 2 ± 9 2. ( a m ) n ± a mn (4 3/2 ) 2 ± 4 (3/2 p 2) ± 4 3 ± 64 3. ( ab ) m ± a m b m (9 p 4) 1/2 ± 9 1/2 p 4 1/2 ± 3 p 2 ± 6 4. a ³ m ± ´ a 1 m ´ , a µ 02 5 ³ 1/2 ± ´ 25 1 1/2 ´ ± ´ 1 5 ´ 5. ´ a a m n ´ ± a m ³ n , a µ 0 ´ 6 6 5 1 / / 2 2 ´ ± 6 (5/2 ³ 1/2) ± 6 2 ± 36 6.
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Algebra 2 7.2 Notes - 7.2 Properties of Rational Exponents...

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