MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C923D2.0BC31B50" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C923D2.0BC31B50 Content-Location: file:///C:/CD28BE65/M117Lesson10.2.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Lesson 10

Lesson 10.2(F&#= 8217;08)

Objectives: To evaluate rational exponen= ts

= To write radical= s as expressions raised to

rational exponen= ts

= To simplify expressions with rational number

= exponents using = the rules of exponents

= To use rational exponents to simplify radical

= expressions=

Rational exponents: An exponent that is a fraction

^{=3D ?&=
nbsp;}

( )² =3D 6 &n= bsp; = ; ( )² =3D 6

Therefore =3D

If b is a real number, n is a positive integer greater than 1, and is a real n= umber, then =3D <= sub>

Example- Express each expression in radical= form.

1. &= nbsp; &nbs= p; &= nbsp; 2.

3. &= nbsp; &nbs= p; &= nbsp; 4.

5. &= nbsp; &nbs= p; &= nbsp; &nbs= p; 6. =

Rewrite using radicals, then simplify.

1. 49^1/2 = 2. 121^1/2 = 3. (-64)^1/3

4. ()^1/2 &= nbsp; 5.

If is a ration= al number, where n is a positive integer greater than 1 and b is a real number such that is a real number, then

&= nbsp; &nbs= p; =3D or

Example-Rewrite using radicals and then evaluate or

= simplify.

1. &= nbsp; &nbs= p; &= nbsp; 2.

Example- Write each expression in radical f= orm.

1. &= nbsp; &nbs= p; &= nbsp; 2.

Example Write each radical using rational exponents.

Recall that a^-b =3D

Negative Rational Exponents

, where a 0and m and n are natural numbers

with n 1.

Rewrite using radical= s, then simplify, if possible.

1. &= nbsp; &nbs= p; 2. &= nbsp; &nbs= p; &= nbsp; 3. =

RULES OF EXPONENTS

If m and n are integers and a and b are real numbers ( and b0 whenever it appears in the denominator), then

1. b⁰ =3D 1 = &nb= sp; 7. =3D b^{n=
–
m}

2. a^-n =3D

3. bⁿ ^.b^m =3D b^{n + m}

4. (bⁿ)^m =3D b<= sup>nm

5. (ab)ⁿ =3D a^n.bⁿ

6. ()ⁿ =3D

Example-Simplify- use only positive exponents.

Often, radical expres= sions can be simplified by rewriting them with rational exponents, simplifying, a= nd then rewriting as a radical expression.

Example-Perform the indicated operation and express the

answer in simplest radical form.

1. &= nbsp; &nbs= p; = 2. &= nbsp; &nbs= p; = 3. =

4 &= nbsp; &nbs= p; 5. &= nbsp; 6.

Write with a single radical.

CW Worksheet 10.2

Homework Math XL Sect= ion 10.2

DUE BY ______________= _______.

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