section 2.8 3.1 powers and exponents - squ root (math)

Sept. 09, 2010 Thursday’s Quiz:

Lesson 2-2 Comparing and Ordering Rational Numbers (compare fractions)

Lesson 2-8 Powers and ExponentsLesson 3-1 Square RootsLesson 3-2 Estimating Square RootsLesson 3-3 The Real Number System (compare

square roots)Lesson 4-1 Ratios and Rates

Section 2.8POWERS and EXPONENTS

Basic Terminology

.

,

.

,

TIONMULTIPLICA

repeatedundergoesthatVariableornumberthenotationlExponentiaInBase

factoraasusedis

basethetimesofnumberthenotationlExponentiaInExponent

42BASE

EXPONENTmeans 162222

Important Examples

IMPORTANT EXAMPLES81)3333(34 means

81)3()3()3()3()3( 4 means

27)333(33 means

27)3()3()3()3( 3 means

Variable Examples

Variable Expressions

))()((

))()()()(()(

3

5

yyymeansy

xxxxxtionmultiplicaforsparentheseusemeansx

Substitution and EvaluatingSTEPS

1.Write out the original problem.2.Show the substitution with parentheses.3.Work out the problem.

3;4: xxifSolveExample 3;4 xxifSolve

3)4( = 64

More Examples

ZERO AND NEGATIVE EXPONENTSANYTHING TO THE ZERO POWER IS 1.

27

1

3

13

9

1

3

13

3

1

3

13

13

33

93

273

33

22

11

0

1

2

3

22222

222

4

1

2

1

)2(

1)2(

2122

xxxx

xxx

8131

31

3

11

311

3

1 44

4

4

4

MULTIPLICATION PROPERTIESPRODUCT OF POWERS

This property is used to combine 2 or more exponential expressions with the SAME base.

53 22 )222( )22222( 82 256

))(( 43 xx ))()(( xxx ))()()(( xxxx 7x

Evaluate the variable expression when x = 1, y = 2, and w = -3

22 )()( yx

22 )()( yx

22 )2()1(

541

Step 1

Step 2

Step 3

2)( yx

2)( yx

2)2()1(

9)3( 2

Step 1

Step 2

Step 3

ywx

ywx

2)1)(3(

Step 1

Step 2

Step 3

3)1)(3(

MULTIPLICATION PROPERTIESPOWER OF PRODUCT

This property combines the first 2 multiplication properties to simplify exponential expressions.

2)56( )5()6( 22 9002536

3)5( xy ))()(5( 333 yx33125 yx

532 )4( xx 5323 ))(4( xx 5222 ))()(()64( xxxx

56 ))(64( xx 1164x

ZERO and NEGATIVE PROPERTIES

Zero power

1)( 0 x

Negative Exponents

aa

aa

xx

andx

x

1

1

Section 3.1

Square Roots

Find each square roots:

√25 -√81 √(4/9)

Solve the equations:

Y2 = 36 E2 = 144S2 = 9 / 25

Classwork / Homework:

Page 100 # 14 – 40 even

Wednesday’s work:Page 118 # 14 – 42 even