Warm Up 10/13

Simplify each expression.

16,807

121

729

1. 73 • 72

3. (32)3

2. 118

116

4.

5.

75

207

2 35

7

5 3

Be seated before the bell rings

DESK

homeworkWarm-up (in your notes)

Agenda:

WarmupNotes 8.6

NotebookTable of content

Page1

1

19)Add, subtract, multiply polynomials

20) Dividing Polynomials

21) Factor and find roots

22) Fundamental Theorem of Algebra

23)Graph of polynomials

24) Radical Expressions and Rational exponents

8.6 Radical Expressions and Rational exponents

HW ;

p.615(3-23 odd)

(35-55 odd)

8.6 radical Expressions and Rational Exponents

1. Find all the square roots of 25

25 2 25x 5x 5x

5 32

2. Find all the fifth roots of 325 32x 2x 2x

3 64

3. Find all the cube roots of -643 64x 4x

4 6254. Find all the fourth roots of -625

4 625x x no solution

n athe nth roots of a

Types of real roots

Case # of roots examples

index

odd 1 real root

even; + radicand

radicand

2 real roots

even; - radicand 0 real roots

Radicand =0 1 real root

5. Find all real roots.

a. fourth roots of –256

negative - no real fourth roots.

Check It Out! Example 1

b. sixth roots of 1

positive - two real sixth roots. X = 1 and –1.

c. cube roots of 125

positive - one real cube root. X= 5.

3 x x x

3x3

Simplifying Radical Expressions

6.

7.

Simplify the expression. Assume that all variables are positive.

2 x

2x

4 416x

4 24 •4 x4

4 24 •x4

8. 9.

84

4 3

x

42

27

3x

10. 3 37 2x x

x3

3 9x

n

ma n ma

5

38 53 8 53 8

52

32

10.

Method 1 Evaluate the root first.

(4)1

6413

4

Write the expression in radical form, and simplify.

Method 2

4

13 64 13 64

3 64

11.

Method 1.

(2)5

452

32

You try!

12.

Method 2

32

52 4 5

2 4

2 1024

6253413.

(5)3

125

34 625

125

34 625

4 244,140,625

Method 1. Method 2

Writing Expressions by Using Rational Exponents

Simplify.

15 5 13

1312 Simplify.

14. 15.

4813

133

2197

m

mn na a m

mn na a

Simplify.

16. 17.

3481

103

You try!

9310

1000

m

mn na am

mn na a

Simplify. 512

18.

24 5

mmn na a

Rational exponents have the same properties as integer exponents

Product of Powers.

Simplify each expression.

19.

Simplify.

Evaluate the Power.

72

49

Check Enter the expression in a graphing calculator.

Simplify each expression.

1

4

6

20. 21. (–8)–

13

22.

1

–8 13

1

2 –

Lesson Quiz:

Find all real roots.

–5, 51. fourth roots of 625

2. fifth roots of –243 –3

Simplify each expression.

2 4. 4y2

5. Write (–216) in radical form and simplify.23

6. Write using rational exponents. 5321

3. 84 256y

= 36 2

3 2163 521