YOUR TURN Simplify and write your answer with only positive exponents 16 x 3 y

Your turn simplify and write your answer with only

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YOUR TURN Simplify and write your answer with only positive exponents. (16 x 3 y ) 1/2 (27 x 2 y 3 ) 1/3 = - 2 x 1/6 3 y 5/3 ( - 8 x 2 y ) 1/3 (9 xy 4 ) 1/2 = ( - 8) 1/3 ( x 2 ) 1/3 y 1/3 9 1/2 x 1/2 ( y 4 ) 1/2 = ( - 8) 1/3 x 2/3 y 1/3 9 1/2 x 1/2 y 2 = a - 2 3 b x 2/3 - 1/2 y 1/3 - 2 = - 2 3 x 1/6 y - 5/3 x 7 0, y 7 0. ( - 8 x 2 y ) 1/3 (9 xy 4 ) 1/2 Answer: 4 x 5/6 3 y 1/2 EXAMPLE 11 Factoring Expressions with Rational Exponents Factor completely . Solution: Factor out the greatest common factor . Factor the trinomial. YOUR TURN Factor completely . x 7/3 - x 4/3 - 2 x 1/3 = x 2/3 ( x - 6)( x + 1) x 2/3 x 8/3 - 5 x 5/3 - 6 x 2/3 = x 2/3 ( x 2 - 5 x - 6) x 8/3 - 5 x 5/3 - 6 x 2/3 EXAMPLE 9 Simplifying Expressions with Negative Rational Exponents Simplify Solution: Negative exponents correspond to positive exponents in the reciprocal. Eliminate the parentheses. Apply the quotient property on x . Simplify. YOUR TURN Simplify x 7 0. 9 x 3/2 (4 x ) - 1/2 = x 12 = x 1 4 # 3 = x 3/2 - 1/2 4 # 9 1/2 = x 3/2 4 # 9 1/2 x 1/2 (9 x ) - 1/2 4 x - 3/2 = x 3/2 4 # (9 x ) 1/2 x 7 0. (9 x ) - 1/2 4 x - 3/2 Answer: x 1/3 ( x - 2)( x + 1) s 3 s x 2/3 x 6/3 s x 2/3 x 3/3
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