1. 6.2 Rational Numbers as Exponents

2. a Index radical Radicand n RADICAL EXPRESSION
Will not shown if it is a square root
radical
Radicand n
RADICAL EXPRESSION

3. Formulas 1 n
a = n a
a = n am
a = m n -m n 1
n am

4. Examples: use the first formula1 2
3 =
2) (-8) =
3) 7 9x =
4) 5 x3y = 4 1 3

5. Answers: 3 = 3 2) (-8) = 3 -8 = -2 3) 7 9x = (9x) 4) 5 x3y = x3y 4 4 1
3 =
2) (-8) = = -2
3) 7 9x = (9x)
4) 5 x3y = x3y 1 3 1 7 1 5

6. Examples: use the 2nd formula3 = =

7. Answers: 2 3
= = = 9
= (-23) 3 5

8. Examples: use the 3rd formula-2 3 1 5
4x y = = -2 3

9. 4x y = 4∙ y1/5 = 64 = 1 = 1 = 1 642/3 3 642 16 Answers: 1 x2/3 4 5 y-2 3 1 5
4x y = 4∙ y1/5 =
= = = 1
642/ 1
x2/3
4 5 y
3 x2 -2 3

10. Review am * an = am+n am = am-n an 3) (am) n = amn 4) (ab) m = ambm
5) a n = an
b bn

11. More examples 21/5 · 23/5 = a1/4 = a1/2 3) (52/3)3/4 =
21/5 · 23/5 =
a1/ =
a1/2
3) (52/3)3/4 =
4) (x-1/3y2/6)1/2 =
5) 3 x =

12. Answers: 21/5 · 23/5 = 24/5 = 5 24 = 5 16 a1/4 = a-1/4 = 1 = 1
21/5 · 23/5 = 24/5 = = 5 16
a1/ = a-1/4 = = 1
a1/ a1/ a
3) (52/3)3/4 = 56/12 = 51/2 = 5
4) (x-1/3y2/6)1/2 = x-1/6y1/6 = y1/6 = 6 y
x1/ x
5) 3 x = x1/3 = x (1/3)/2 = x1/6 = 6 x