4/12/10 swbat… compute problems involving zero & negative exponents agenda 1. write hw in...
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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
Monomials
Ms. Sophia Papaefthimiou
Infinity HS
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, 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
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
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
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
This exponent is read three to the fourth power.
34
How to read an exponent (cont’d)
This exponent is read three to the 2nd power or three squared.
32
How to read an exponent (cont’d)
This exponent is read 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) Length = 30 ftWidth = 15 ft
Area = (30 ft)(15 ft) = 450 ft 2
15ft
30ft
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
What is the exponent?
(5)(5)(5)(5) = 54
What is the base and the exponent?
(7)(7)(7)(7)(7) = 7 5
What is the answer?
53
= 125
Compute: 02
Answer: (0)(0) = 0
Compute: (-4)2
Answer: (-4)(-4) = 16
Compute: -42
Answer: -(4)(4) = -16
Compute: 20
Answer: 1Yes, 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.) 60 = 1
3.) -60 = -1
5.) 6.) 10
c
b1
7
20
2.) (-6)0 = 1
4.) (abc)0 = 1
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
WHY is anything to the power zero "1"
35 = 243
34 = 81
33 = 27
32 = 9
31 = 3
30 =
30 = 1
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
52
1
52 32
Examples (cont’d)
24
1
24 16
112
12
1
4848
1
4096
1
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
OYO Problems 24
0)2(3222)16(
12
1