CHAPTER 8: EXPONENTS AND POLYNOMIALS

Chapter 8

CHAPTER 8: EXPONENTS AND POLYNOMIALS

Chapter Objectives By the end of this chapter, students should be able to:

Simplify exponential expressions with positive and/or negative exponents Multiply or divide expressions in scientific notation Evaluate polynomials for specific values Apply arithmetic operations to polynomials Apply special-product formulas to multiply polynomials Divide a polynomial by a monomial or by applying long division

CHAPTER 8: EXPONENTS AND POLYNOMIALS ........................................................................................ 211 SECTION 8.1: EXPONENTS RULES AND PROPERTIES ........................................................................... 212 A. PRODUCT RULE OF EXPONENTS .............................................................................................. 212 B. QUOTIENT RULE OF EXPONENTS ............................................................................................. 212 C. POWER RULE OF EXPONENTS .................................................................................................. 213 D. ZERO AS AN EXPONENT............................................................................................................ 214 E. NEGATIVE EXPONENTS............................................................................................................. 214 F. PROPERTIES OF EXPONENTS .................................................................................................... 215 EXERCISE ........................................................................................................................................... 216 SECTION 8.2 SCIENTIFIC NOTATION..................................................................................................... 217 A. INTRODUCTION TO SCIENTIFIC NOTATION ............................................................................. 217 B. CONVERT NUMBERS TO SCIENTIFIC NOTATION ..................................................................... 218 C. CONVERT NUMBERS FROM SCIENTIFIC NOTATION TO STANDARD NOTATION .................... 218 D. MULTIPLY AND DIVIDE NUMBERS IN SCIENTIFIC NOTATION ................................................. 219 E. SCIENTIFIC NOTATION APPLICATIONS..................................................................................... 220 EXERCISE ........................................................................................................................................... 222 SECTION 8.3: POLYNOMIALS................................................................................................................ 223 A. INTRODUCTION TO POLYNOMIALS ......................................................................................... 223 B. EVALUATING POLYNOMIAL EXPRESSIONS .............................................................................. 225 C. ADD AND SUBTRACT POLYNOMIALS ....................................................................................... 226 D. MULTIPLY POLYNOMIAL EXPRESSIONS ................................................................................... 228 E. SPECIAL PRODUCTS .................................................................................................................. 230 F. POLYNOMIAL DIVISION............................................................................................................ 231 EXERCISE ........................................................................................................................................... 237 CHAPTER REVIEW ................................................................................................................................. 239

211

SECTION 8.1: EXPONENTS RULES AND PROPERTIES A. PRODUCT RULE OF EXPONENTS

Chapter 8

MEDIA LESSON Product rule of exponents (Duration 2:57)

View the video lesson, take notes and complete the problems below 3 2 = ( )( ) = 5

Product rule: = +

____________________________!

Example 1: (2x3)(4x2)(-3x) = ___________________________

Example 2: (5a3b7)(2a9b2c4) = ___________________________

Warning! The rule can only apply when you have the same base.

YOU TRY

Simplify: a) 53510

b) 132

c) (235)(523)

B. QUOTIENT RULE OF EXPONENTS

MEDIA LESSON Quotient rule of exponents (Duration 3:12)

View the video lesson, take notes and complete the problems below

Quotient

Rule:

=

-

5 3

=

=

2

_________________________________

72 Example 1: 3

874

Example 2: 65

= ___________________________

= ___________________________

YOU TRY

Simplify

713

a) 75

5352

b) 23

35

c) 3

212

C. POWER RULE OF EXPONENTS MEDIA LESSON Power rule of exponents (Duration 5:00)

View the video lesson, take notes and complete the problems below

(ab)3=_____________________________ = ________

Power of a product: () =

3=____________________ =_____________

Power of a Quotient:

=

, if b is not 0.

(2)3 = _____________________ = ______

Power of a Power: () =

Example 1: (54)3

Example

2:

5943

2

Chapter 8

Warning! It is important to be careful to only use the power of a product rule with multiplication inside parenthesis. This property is not allowed for addition or subtraction, i.e.,

YOU TRY

( + ) + ( - ) -

Simplify:

a) 325

b) 25327

c) (32)4

d) (425)3

e) 835 2

f) 482

213

D. ZERO AS AN EXPONENT

MEDIA LESSON Zero as Exponent (Duration 3:51)

View the video lesson, take notes and complete the problems below

33=_____________________________________________ Zero Power Rule: =

Example 1: (535)0

Example 2: (320)(504)

Chapter 8

YOU TRY

Simplify the expressions completely a) (3x2)0

206

b) 35

E. NEGATIVE EXPONENTS

MEDIA LESSON Negative Exponents (Duration 4:44)

View the video lesson, take notes and complete the problems below

3

5 = __________________________________________ =___________________________________________

Negative Exponent Rule:

-

=

When a and b are not 0.

1 - =

-

= =

7-5

Example 1: 3-1-4

2

Example 2: 5-4

Warning! It is important to note a negative exponent does not imply the expression is negative, only the reciprocal of the base. Hence, negative exponents imply reciprocals.

YOU TRY

3

a) 5-1

32

b) 2-1-4

214

Chapter 8

F. PROPERTIES OF EXPONENTS Putting all the rules together, we can simplify more complex expression containing exponents. Here we apply all the rules of exponents to simplify expressions.

Product = +

Power of a Product () =

Negative Power

- =

Exponent Rules

Quotient

=

-

Power of a Quotient =

Reciprocal of Negative Power

-

=

Power of Power () =

Zero Power =

Negative Power of a Quotient

-

= =

MEDIA LESSON Properties of Exponents (Duration 5:00)

View the video lesson, take notes and complete the problems below

Example 1: (4x5y2z)2(24-23)4

2x2y34x4y-6-2

Example 2:

(x-6y4)2

YOU TRY

Simplify and write your final answers in positive exponents.

4-5-333-2

a)

6-53

33-2-3

b)

2-40

215

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