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Algebra 2 7.2 Notes

# 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 n 3 1/2 p 3 3/2 3 (1/2 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 m a 1 m , a 0 25 1/2 25 1 1/2 1 5 5. a a m n a m n , a 0 6 6 5 1 / / 2 2 6 (5/2 1/2) 6 2 36 6. a b m a b m m , b 0 2 8 7 1/3 2 8 7 1 1 / / 3 3 2 3 Lesson 7.2 Algebra 2 Notetaking Guide 155

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Your Notes Use properties of rational exponents to simplify the expression.
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