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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3/23/10SWBAT… 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.
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
• 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
• This exponent is read three to the fourth power.

4

3

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

3

3

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

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?

4

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

5

Compute: 02

Compute: (-4)2

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

Compute: -42

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

Compute: 20

Yes, 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.) 120 = 1

2.)

3.)

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: