3/23/10 SWBAT… compute problems involving zero & negative exponents

Monday, 3/15 Tuesday, 3/16 Wednesday, 3/17 Thursday, 3/18 Friday, 3/19

Review ineq testsGet Ready for Ch 7

Exponents OverviewZero ExponentsNegative Exponents

½ Day: BMidterm Outline

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

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


NIU Field TripPolynomials ½ Day: A Adding and

subtracting polynomials

Multiplying polynomials by monomials


SPRING BREAK!!!


Review ineq testsGet Ready for Ch 7

Exponents OverviewZero ExponentsNegative Exponents

½ Day: BMidterm Outline

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

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


NIU Field TripPolynomials ½ Day: A Adding and

subtracting polynomials

Multiplying polynomials by monomials


SPRING BREAK!!!


MIDTERM No ClassesEnd of Quarter

3/23/10SWBAT… compute problems involving zero & negative exponents

Agenda

1. Lesson on monomials and exponents (40 min) Zero Exponents Negative Exponents

HW1: Zero and negative exponents

Monomials

Ms. Sophia Papaefthimiou

Infinity HS

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.

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

An expression that involves division by a variable, like is not a monomial.

c

ab

Determine whether each expression is a monomial. Say 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.

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)

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 feet 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 centimeters 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

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 PropertyWords: Any nonzero number raised to the zero

power is equal to 1.

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

Examples:

1.) 120 = 1

2.)

3.)1

0

c

b

17

20

OYO Problems (On Your Own)

Simplify each expression:

1.) (-4)0

2.) -40

3.) (-4.9)0

4. [(3x4y7z12)5 (–5x9y3z4)2]0

WHY is anything to the power zero "1"

35 = 36 ÷ 3 = 36 ÷ 31 = 36–1 = 35 = 243 34 = 35 ÷ 3 = 35 ÷ 31 = 35–1 = 34 = 81 33 = 34 ÷ 3 = 34 ÷ 31 = 34–1 = 33 = 27 32 = 33 ÷ 3 = 33 ÷ 31 = 33–1 = 32 = 9 31 = 32 ÷ 3 = 32 ÷ 31 = 32–1 = 31 = 3

30 = 30 = 31 ÷ 3 = 31 ÷ 31 = 31–1 = 30 = 1

Negative Exponent Property

Words: For any nonzero number a and any integer n, a-n is the reciprocal of an. Also, the reciprocal of a-n = an.

Symbols: For any nonzero number a and any integer n,

Examples:

nnn

n aa

anda

a 11

25

1

5

15

22 3

3

1m

m

24

18

2

1828

22

OYO Problems (On Your Own)

24

0)2(3222)16(

3/23/10 SWBAT… compute problems involving zero & negative exponents

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