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4/12/10SWBAT… compute problems involving zero & negative exponents
Agenda
1. Write hw in planner
2. Review hw#5 (10 min)
3. Quiz on compound and graphing inequalities (10 min)
4. Get Ready for Chapter 7 (5 min)
5. Lesson on monomials and exponents (25 min) Zero Exponents Negative Exponents
HW1: Zero and negative exponents
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Monomials
Ms. Sophia Papaefthimiou
Infinity HS
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Monday, 4/12 Tuesday, 4/13 Wednesday, 4/14 Thursday, 4/15 Friday, 4/16
Get Ready for Ch 7
Exponents Overview
Zero ExponentsNegative Exponents
½ Day: B Zero and negative exponents practice
Quiz on zero and negative exponents
Multiplying MonomialsProduct of Powers (1)Power of a Product (2)Power of a Power (3)
Monday, 4/19 Tuesday, 4/20 Wednesday, 4/21 Thursday, 4/22 Friday, 4/23
Multiplying monomials practice
Dividing MonomialsPower of a Quotient (4)Quotient of Powers (5)
Dividing monomials practice
Quiz on mult/div
monomials
NO CLASSES – Parent-Teacher
Conferences
PolynomialsStandard fromTermsDegrees
Monday, 4/26 Tuesday, 4/27 Wednesday, 4/28 Thursday, 4/29 Friday, 4/30
GAINS testing9th and 10th graders
GAINS testing9th and 10th graders
NO CLASSES – PSAE testing for
11th graders
NO CLASSES – PSAE testing for 11th
graders
Adding and subtracting polynomials
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Monday, 4/12 Tuesday, 4/13 Wednesday, 4/14 Thursday, 4/15 Friday, 4/16
Get Ready for Ch 7
Exponents Overview
Zero ExponentsNegative Exponents
½ Day: B Zero and negative exponents practice
Quiz on zero and negative exponents
Multiplying MonomialsProduct of Powers (1)Power of a Product (2)Power of a Power (3)
Monday, 4/19 Tuesday, 4/20 Wednesday, 4/21 Thursday, 4/22 Friday, 4/23
Multiplying monomials practice
Dividing MonomialsPower of a Quotient (4)Quotient of Powers (5)
Dividing monomials practice
Quiz on mult/div
monomials
NO CLASSES – Parent-Teacher
Conferences
PolynomialsStandard fromTermsDegrees
Monday, 4/26 Tuesday, 4/27 Wednesday, 4/28 Thursday, 4/29 Friday, 4/30
GAINS testing9th and 10th graders
GAINS testing9th and 10th graders
NO CLASSES – PSAE testing for
11th graders
NO CLASSES – PSAE testing for 11th
graders
Adding and subtracting polynomials
Monday, 5/3 Tuesday, 5/4 Wednesday, 5/5 Thursday, 5/6 Friday, 5/7
Multiplying polynomials by monomials
Multiplying two binomials (FOIL)
½ Day: A Additional practice: FOIL
Investigation: Special products
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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. An expression that involves division by a
variable, like is not a monomial.
Examples of monomials: 3, s, 3s, 3sp
c
ab
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Determine whether each expression is a monomial. Write 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 (h2 = h ∙ h)
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) = 81
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 units 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 units 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)(0) = 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 Property
Words: Any nonzero number raised to the zero power is equal to 1.
Symbols: For any nonzero number a, a0 = 1.
Examples:1.) 60 = 1
3.) -60 = -1
5.) 6.) 10
c
b1
7
20
2.) (-6)0 = 1
4.) (abc)0 = 1
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OYO Problems
Simplify each expression:
1. (-4)0
2. -40 (Recall PEMDAS - Exponents first!)
3. (5x)0 5x0
4. (-4.9)0 (Recall PEMDAS – Parenthesis first!)
5. [(3x4y7z12)5 (–5x9y3z4)2]0
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WHY is anything to the power zero "1"
35 = 243
34 = 81
33 = 27
32 = 9
31 = 3
30 =
30 = 1
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Negative Exponent PropertyWords: For any nonzero number a and any integer n,
a-n is the reciprocal of an.
Also, an is the reciprocal of a-n.
Symbols:
Examples:
nn
aa
1
25 33
1m
m25
1
5
12
nna
a
1
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52
1
52 32
Examples (cont’d)
24
1
24 16
112
12
1
4848
1
4096
1
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22
18
4
18 2228
Examples (cont’d)
24
4 24
14 244 164 64
0)6(9 )1(9 9
2
2
8
2
22
8
12
22
82
1 64
4
1 14
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OYO Problems 24
0)2(3222)16(
12
1