1. Rational (fraction) exponents 6.4 We’ve worked with positive and negative exponents-- now, let’s move to fractions

2. POD to start Simplify 1.x 3 /x 5 2.x 3 x 5 3.x 5 /x 5 4.x 3(1/3)

3. POD to Start What does x (1/3) look like? A square root means what? So, a cube root means what?

4. Review of negative exponents x -n = 1/x n so, what is 1/x -n ? Try it. Find 2 -5. Now find 1/2 -5.

5. Now, rational (fraction) exponents What does x 2 looks like? What does x 1/3 look like? For the Crown o’ Knowledge, raise your hand and tell me what x 2/3 looks like.

6. Rational exponents x 1/n = n √x x a/n = n √x a = ( n √x) a where n is the root index and x is the radicand. Note how the exponents are fractions.

7. Rational exponents You can use your calculators to find approximate answers. To the board! 4 √2 3 = (437) 1/5 = 7 √423 7 = 6 √99735 =

8. Simplifying Simplify the following, using all your exponential skills. To the board again! 1.(6x 5 )(3x -2 ) 2.(5x -4 )(2x -3 ) 3.(-2x 2 ) 3 (3x -1 y 2 ) 4 4.(x -1 y -4 z)/(x -2 yz -3 ) (How do you subtract a negative number?) 5.(3x -1/2 )(4x 2/3) 6.(3758x 89 )(3758x -89 ) 7.(u 3.7 p 4.8 )/(u -2.9 p 1.8 )