Powers, Roots, & Radicals

OBJECTIVE: To Evaluate and Simplify using properties of exponents and radicals.

Rational Numbers: can be written as a ratio.

Rational Expression:

Rational Function:

2 5 4 11, , , , 0.25, 0.333...,

3 21 1 9etc

3 2

2

8 7

3 5 14

x x xf x

x x

6 5,

1

x

x x

n a Radicand

Index

1 nn a a1 4 4 481 81 3 3 3 3 3

1mmm n n na a a

333 2 1 2 39 9 9 3 27

Simplest Form – properties of radicals have been applied, perfect nth powers have been removed, and any denominators have been rationalized.

Like Radicals – radical expressions that have the same index and the same radicand.

Example: 31/2 . 33/2

Example: (43/2)2

Example: (9 . 4)1/2

Example: 25 -1/2

1, 0

ma

a

Example:

0m

n

aa

a

5/2

1/2

6

6

Example

, 0m m

m

a ab

b b

1/38

27

Property:

Use the properties of rational exponents to simplify the expressions. a.

b.

c.

1/2 1/45 5

21/2 1/38 5

1/44 42 3

1. 27 12 Can only combine like terms! Goal is to simplify each term to see if “life terms” result. “Like radicals” have the same index and the same radicand.

332. 16 2

63

8 4 104

4

48

1. 250

2. 64

3.

y

a b c

x

y

3 35 22. 3 5 40x x x

651. 6 7y y

Read Section 7.2 Pgs. 411-14: 24-81 (x3)