Warm-up. Wed. Jan 26

Recall:Exponent

PROPERTIESaman = am+n

(am)n = amn

(ab)n = an bn

am/an = am-n

3152 zxx

Simplify Completely. No zero or negative exponents

1.

2.

2

2222

2

3)(

zyx

yzx

Review

124 2 x

124

124

x

x

Recall: To solve a quadratic equation like the following, use a square root method:

Goal for this lesson: Radical equation such as:

327 x

Review: Laws of Exponents

aman amn

am

an am n

(am )n amn

(ab)m ambm

ab

m

am

bm

a m 1

am

Section A.9 nth Roots; Rational Exponents; Radical Equations1. nth Root2. Evaluating nth roots3. Properties of nth roots4. Solving Radical Equations5. Rationalize Denominators

6. Fractional Exponentsa) Simplifying Fractional Exponentsb) Simplifying radicals using rational exponents

7. Simplify radicals some morea) 2 methodsb) More practice

1. nth Roots283

cubed root of 8 is 2 2325 3225

3814 8134

823

ban nba

Definition The principal nth root of a number

is defined as:a

2. Evaluating nth Roots

3251)

6432)

116

43)

3. Properties of nth Roots

ab

n an

bn

abn an bn

amn an m

Product Rule for nth Roots

Quotient Rule for nth Roots

3 a) Practice simplifying radicals

32 1)

3

85 2)

3 58 3)

3 b) Multiplying and Combining Radicals

2 6 5 30 1)

5 3 5 2 2)

4. Solving Radical Equations

521 xSolve the following equation.

Isolate radical to one side of equation

Raise both sides to power equal to index of radicand

Check for extraneous solutions

4. Solving Equations with Roots

1 3t3 2 0Solve the following equation.

Isolate radical to one side of equation

Raise both sides to power equal to index of radicand

Check for extraneous solutions

4. Solving Equations with Roots

12 x xSolve the following equation.

Goal: Remove radicals in the denominators

5. Rationalizing Denominators

64

252

Key Idea: For a denominator of the form

Multiply numerator and denominator by:

ba

ba

6. Fractional Exponents

a1

n an

If a is a real number and is an integer, then

n 2

If a is a real number and m and n are integers containing no common factors, with , then,

n 2

mnn mnm

aaa

Ex : 85 3

6 a) Simplifying Fractional ExponentsSimplify the following expressions.

81 5 41)

278

4 32)

6 b) Simplifying Fractional ExponentsSimplify the following expressions.

2/124/143 yxyx

6 c) Practice simplifying radicals using rational exponents

32 1)

3

85 2)

3 58 3)

Examples.Rewrite each radical using rational exponents and simplify.

Day 2: Warm-up

hVr3

Solve the following formula for V:

Solve the following formula for A:

4Ar

2/12344/3 yxyxSimplify:

7. a) Simplify Radicals – 2 methods

Method 1: Look for powers of each term that match the

root.3 458 yx

Method 2:Rewrite using rational exponents and simplify.

3 458 yx

7 a) Simplify Radicals4

3

79

483

xyyx

7 b) Practice Simplifying Radicals

16x 4 y1031) 2) 443 103

7 b) More practice Simplifying Radicals

36x 4 y3 60x 3y 233)

8. Factoring Fractional ExponentsFactor out the GCF.

2/12/3 232323 xxx

8. Factoring Fractional ExponentsFactor out the GCF.

3/52/13/22/12 122121224 xxxxxx