SWBAT… review exponents Tues, 4/9

Agenda 1. WU (10 min)2. Exponent review (25 min)

Warm-Up:1. Write your HW in your planner for the week

2. Write the formula for the area of a rectangle

3. Write the formula for the area of a triangle

4. Write the formula for the area of a circle

5. Write the formula for the circumference of a circle

6. Write the formula for the volume of a rectangular prism

See agenda

New unit on Polynomials & Exponents SWBAT…n Identify the difference between monomials,

binomials and trinomials.n Apply and explain the rules of exponents (7rules) n Add and subtract polynomials.n Multiply a monomial by a polynomial.n Solve equations with polynomials.n Multiply two binomials using the FOIL method.

A monomial is an algebraic expression consisting of only one term.

A term may be a number, a variable, or a product or quotient of numbers and variables (separated by a + or –)

Examples of monomials: 3, s, 3s, 3sp, 3s2p

Open Ended: Write 3 different examples of monomials

Polynomials

A polynomial is a monomial or the sum or difference of monomials

Some polynomials have special names: A monomial has one termA binomial is the sum or difference of two

monomialsA trinomial is the sum or difference of three

monomials

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz

-6.5

6x3 + 4x + x + 3

3ab5

Fill out the chart above!Fill out the chart above!

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5

6x3 + 4x + x + 3

3ab5

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3

3ab5

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3

3ab5

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3 Yes; 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials

Trinomial

3ab5

Expression Is it a polynomial?

Explain

Monomial, binomial, or trinomial?

4y – 5xz Yes; 4y – 5xz is the difference of two monomials.

Binomial

-6.5 Yes; -6.5 is a constant Monomial

6x3 + 4x + x + 3 Yes; 6x3 + 4x + x + 3 = 6x3 + 5x + 3, the sum of three monomials

Trinomial

3ab5 Yes; one term with the product of a coefficient and variables.

Monomial

Exponent Review

Ms. Sophia Papaefthimiou

Infinity HS

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

Three to the fourth power

34

How to read an exponent (cont’d)

Three to the 2nd power or Three squared

32

How to read an exponent (cont’d)

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)

Area = (30 ft)(15 ft) = 450 ft 215ft

30ft

A = π(8cm)2

A = 64π cm2

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

Volume = (length)(width)(height)

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

10

10

20

What is the exponent?

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

What is the answer?

53

= 125

What is the base and the exponent?

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

What is the base and the exponent?

(x)(x)(x)(x)(x)(x) =x 6

What the base and the exponent?

(a)(a)(a)(b)(b)(c) =a 3b2c

What the base and the exponent?

aaabbc = a 3b2c

What the base and the exponent?

(4)(x)(x)(y) = 4x 2y

What the base and the exponent?

(4xxyyyy)(8xxy) = 32 x 4y 5

Compute: (-4)2

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

Calculate: -42

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

PEMDAS

Simplify: n2 when n = -5

Answer: (-5)2 = (-5)(-5) = 25

Simplify: -n2 when n = -5

Answer: -(-5)2 = -(-5)(-5) = -25

Compute: (-6)2

Answer: (-6)(-6) = 36

Compute: -62

Answer: -(6)(6) = -36

Compute: -(-6)2

Answer: -(-6)(-6) = -36

Simplify: (x + 3)2

Answer: (x + 3)(x + 3) x2 + 6x + 9

Compute: 02

Answer: (0)(0) = 0

Compute: 20

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

WHY is anything to the power zero "1"

36 = 72935 = 243 34 = 81 33 = 27 32 = 9 31 = 3

30 = 1

Laws of Exponents

nmn

m

m

mm

mmm

mnnmnmnm

nnn

n

xx

x

y

x

y

xyxxy

xxxxx

xx

orx

xx

.7

.6.5

.4.3

11.21.1 0

Zero Exponent Property (1)Words: 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

Open Ended: Create a problem that satisfies this property!

Let’s practice

Simplify each expression:

1. (-4)0

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

3. (5x)0 5x0

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

5. [(3x4y7z12)5 (–5x9y3z4)2]0

Negative Exponent Property (2)

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

Open Ended: Create a problem that satisfies this property!Use any number for a and n.

52

152 32

Examples

24

1

24 16

112

12

1

4848

1

4096

1

3)2(

1

3)2( )2)(2)(2(

1

8

1

2

2

7

2

06 yx

SWBAT… compute problems involving zero & negative exponents Fri, 4/27

Agenda 1. Review problems Zero & Negative Exponent Property (20 min)

2. Practice – hw#1 (15 min)

3. Quiz (10 min)

WARM-UP

1. (5x)0

2. 5x0

3.4.

HW: Quiz corrections

0)( iouPapaefthimSophia3)2(

22

1

1

8

4

1

1

8 2228

Examples (cont’d)

24

4 24

1

1

4 244 164 64

0)6(9 )1(9 9

2

2

8

2

2

2

8

1

1

2

22

82

1 64

4

1 16

SWBAT… simplify problems using the first 5 exponent laws Wed, 5/2Agenda

1. WU (5 min)

2. Review HW#1 (15 min) and Review HW#2 (20 min)

3. Exit slip (5 min)

Warm-Up: Simplify:

03 )2(32 d

29