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

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

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3 23 10 swbat compute problems involving zero negative exponents

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

Monomials

Ms. Sophia Papaefthimiou

Infinity HS


3 23 10 swbat compute problems involving zero negative exponents

  • 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.


Determine whether each expression is a monomial say yes or no explain your reasoning

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

1.) 10

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

2.) f + 24

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

3.) h2

3.) Yes, this expression is a product of variables.

4.) j

4.) Yes, single variables are monomials.

5.)

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


Definition of an exponent

Definition of an exponent

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

4

Exponent

3

Base

4

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

3


How to read an exponent

How to read an exponent

  • This exponent is read three to the fourth power.

4

3


How to read an exponent cont d

How to read an exponent (cont’d)

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

2

3


How to read an exponent cont d1

How to read an exponent (cont’d)

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

3

3


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

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

Area = (length)(width)

Length = 30 ft

Width = 15 ft

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

15ft

30ft

2


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

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

Volume = (length)(width)(height)

Length = 10 cm

Width = 10 cm

Height = 20 cm

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

20

10

10

3


What is the exponent

What is the exponent?

4

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

5


What is the base and the exponent

What is the base and the exponent?

5

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

7


What is the answer

What is the answer?

3

5

125

=


3 23 10 swbat compute problems involving zero negative exponents

Compute: 02

Answer: 0


3 23 10 swbat compute problems involving zero negative exponents

Compute: (-4)2

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


3 23 10 swbat compute problems involving zero negative exponents

Compute: -42

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


3 23 10 swbat compute problems involving zero negative exponents

Compute: 20

Answer: 1

Yes, it’s 1…explanation will follow


Zero exponent property

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.) 120 = 1

2.)

3.)


Oyo problems on your own

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

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

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:


Oyo problems on your own1

OYO Problems (On Your Own)


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