10.3: rational exponents April 27, 2009

Objectives 1.Define rational exponents 2.Simplify expressions that contain rational exponents 3.Estimate the value of an expression using a calculator 4.Write expressions in radical or exponential form, interchangeably

Rational numbers as exponents Rational numbers are also called: Consider: a = 9 1/2 what would you do to both sides? (a) 2 =(9 1/2 ) 2 a 2 = 9 a=3 So… 3=9 1/2 Fraction s!

Rules for rational exponents a 1/n = n √a a m/n = n √a m Remember these previously discussed rules: a m *a n = a m+n a m /a n = a m-n (a m ) n = a m*n (ab) m = a m *b m (a/b) m = a m /b m

Write in radical form, then simplify 25 1/2 27 1/3 9 3/2 (16/81) 3/4 (-8) 2/ / /3

Additional rules x 2/3 * x 1/2 x 3/4 x 1/2 (x 2/3 ) 3/4

Even trickier (x 2/3 *y 5/6 ) 3/2

Write in radical form a 3/5 (mn) 3/4 2y 5/6 (2y) 5/6

Write in exponential form 3 √(5x) √(9a 2 b 4 ) 4 √(16w 12 z 8 )

Your assignment p #14-76even