4/12/10 SWBAT… compute problems involving zero & negative exponents

4/12/10SWBAT… compute problems involving zero & negative exponents

Agenda

1. Write hw in planner

2. Review hw#5 (10 min)

3. Quiz on compound and graphing inequalities (10 min)

4. Get Ready for Chapter 7 (5 min)

5. Lesson on monomials and exponents (25 min) Zero Exponents Negative Exponents

HW1: Zero and negative exponents

Monomials

Ms. Sophia Papaefthimiou

Infinity HS

Monday, 4/12 Tuesday, 4/13 Wednesday, 4/14 Thursday, 4/15 Friday, 4/16

Get Ready for Ch 7

Exponents Overview

Zero ExponentsNegative Exponents

½ Day: B Zero and negative exponents practice

Quiz on zero and negative exponents

Multiplying MonomialsProduct of Powers (1)Power of a Product (2)Power of a Power (3)


Multiplying monomials practice

Dividing MonomialsPower of a Quotient (4)Quotient of Powers (5)

Dividing monomials practice

Quiz on mult/div

monomials

NO CLASSES – Parent-Teacher

Conferences

PolynomialsStandard fromTermsDegrees


GAINS testing9th and 10th graders


NO CLASSES – PSAE testing for

11th graders

NO CLASSES – PSAE testing for 11th

graders

Adding and subtracting polynomials


Get Ready for Ch 7

Exponents Overview

Zero ExponentsNegative Exponents

½ Day: B Zero and negative exponents practice

Quiz on zero and negative exponents

Multiplying MonomialsProduct of Powers (1)Power of a Product (2)Power of a Power (3)


Multiplying monomials practice

Dividing MonomialsPower of a Quotient (4)Quotient of Powers (5)

Dividing monomials practice

Quiz on mult/div

monomials

NO CLASSES – Parent-Teacher

Conferences

PolynomialsStandard fromTermsDegrees




NO CLASSES – PSAE testing for

11th graders

NO CLASSES – PSAE testing for 11th

graders

Adding and subtracting polynomials


Multiplying polynomials by monomials

Multiplying two binomials (FOIL)

½ Day: A Additional practice: FOIL

Investigation: Special products

A monomial is a number, a variable or the product of a number and one or more variables with nonnegative integer exponents.

It has only one term. An expression that involves division by a

variable, like is not a monomial.

Examples of monomials: 3, s, 3s, 3sp

c

ab

Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.

1.) 101.) Yes, this is a constant, so it is a monomial.

2.) f + 242.) No, this expression has addition, so it has more than one term.

3.) h2

3.) Yes, this expression is a product of variables (h2 = h ∙ h)

4.) j4.) Yes, single variables are monomials.

5.)

5.) No, this expression has a variable in the denominator.n

mp

Definition of an exponent

An exponent tells how many times a number is multiplied by itself.

34

= (3)(3)(3)(3) = 81

34

BaseExponent

How to read an exponent

This exponent is read three to the fourth power.

34

How to read an exponent (cont’d)

This exponent is read three to the 2nd power or three squared.

32

How to read an exponent (cont’d)

This exponent is read three to the 3rd power or three cubed.

33

Exponents are often used in area problems to show the units are squared

Area = (length)(width) Length = 30 ftWidth = 15 ft

Area = (30 ft)(15 ft) = 450 ft 2

15ft

30ft

Exponents are often used in volume problems to show the units are cubed

Volume = (length)(width)(height) Length = 10 cmWidth = 10 cmHeight = 20 cm

Volume = (20cm)(10cm)(10cm) = 2,000 cm3

10

10

20

What is the exponent?

(5)(5)(5)(5) = 54

What is the base and the exponent?

(7)(7)(7)(7)(7) = 7 5

What is the answer?

53

= 125

Compute: 02

Answer: (0)(0) = 0

Compute: (-4)2

Answer: (-4)(-4) = 16

Compute: -42

Answer: -(4)(4) = -16

Compute: 20

Answer: 1Yes, it’s 1…explanation will follow

Zero Exponent Property

Words: Any nonzero number raised to the zero power is equal to 1.

Symbols: For any nonzero number a, a0 = 1.

Examples:1.) 60 = 1

3.) -60 = -1

5.) 6.) 10

c

b1

7

20

2.) (-6)0 = 1

4.) (abc)0 = 1

OYO Problems

Simplify each expression:

1. (-4)0

2. -40 (Recall PEMDAS - Exponents first!)

3. (5x)0 5x0

4. (-4.9)0 (Recall PEMDAS – Parenthesis first!)

5. [(3x4y7z12)5 (–5x9y3z4)2]0

WHY is anything to the power zero "1"

35 = 243

34 = 81

33 = 27

32 = 9

31 = 3

30 =

30 = 1

Negative Exponent PropertyWords: For any nonzero number a and any integer n,

a-n is the reciprocal of an.

Also, an is the reciprocal of a-n.

Symbols:

Examples:

nn

aa

1

25 33

1m

m25

1

5

12

nna

a

1

52

1

52 32

Examples (cont’d)

24

1

24 16

112

12

1

4848

1

4096

1

22

18

4

18 2228

Examples (cont’d)

24

4 24

14 244 164 64

0)6(9 )1(9 9

2

2

8

2

22

8

12

22

82

1 64

4

1 14

OYO Problems 24

0)2(3222)16(

12

1

4/12/10 SWBAT… compute problems involving zero & negative exponents

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