3/23/10 swbat… compute problems involving zero & negative exponents
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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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)
Monday, 3/22 Tuesday, 3/23 Wednesday, 3/24 Thursday, 3/25 Friday, 3/26
NIU Field TripPolynomials ½ Day: A Adding and
subtracting polynomials
Multiplying polynomials by monomials
Monday, 3/29 Tuesday, 3/30 Wednesday, 3/31 Thursday, 4/1 Friday, 4/2
SPRING BREAK!!!
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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)
Monday, 3/22 Tuesday, 3/23 Wednesday, 3/24 Thursday, 3/25 Friday, 3/26
NIU Field TripPolynomials ½ Day: A Adding and
subtracting polynomials
Multiplying polynomials by monomials
Monday, 3/29 Tuesday, 3/30 Wednesday, 3/31 Thursday, 4/1 Friday, 4/2
SPRING BREAK!!!
Monday, 4/5 Tuesday, 4/6 Wednesday, 4/7 Thursday, 4/8 Friday, 4/9
MIDTERM No ClassesEnd of Quarter
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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
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Monomials
Ms. Sophia Papaefthimiou
Infinity HS
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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
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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
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Definition of an exponent
An exponent tells how many times a number is multiplied by itself.
34
= (3)(3)(3)(3)
34
BaseExponent
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How to read an exponent
This exponent is read three to the fourth power.
34
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How to read an exponent (cont’d)
This exponent is read three to the 2nd power or three squared.
32
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How to read an exponent (cont’d)
This exponent is read three to the 3rd power or three cubed.
33
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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
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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
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What is the exponent?
(5)(5)(5)(5) = 54
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What is the base and the exponent?
(7)(7)(7)(7)(7) = 7 5
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What is the answer?
53
= 125
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Compute: 02
Answer: 0
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Compute: (-4)2
Answer: (-4)(-4) = 16
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Compute: -42
Answer: -(4)(4) = -16
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Compute: 20
Answer: 1Yes, it’s 1…explanation will follow
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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
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OYO Problems (On Your Own)
Simplify each expression:
1.) (-4)0
2.) -40
3.) (-4.9)0
4. [(3x4y7z12)5 (–5x9y3z4)2]0
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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
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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
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24
18
2
1828
22
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OYO Problems (On Your Own)
24
0)2(3222)16(