Transcript Zero and Negative Exponents

Exponents
EQ: How can you evaluate negative
exponents?
Definition of an exponent
 An
exponent tells how many times a
number is multiplied by itself.
4
Base
4
3
Exponent
3 = (3)(3)(3)(3) = 81
How to read an exponent
 Three
to the fourth power
4
3
How to read an exponent (cont’d)
to the 2nd power or
 Three squared
 Three
2
3
How to read an exponent (cont’d)
 Three
to the 3rd power or
 Three cubed
3
3
Exponents are often used in area
problems to show the units are squared
Area = (length)(width)
15ft
Length = 30 ft
Width = 15 ft
30ft
2
Area = (30 ft)(15 ft) = 450 ft
A=
2
π(8cm)
A = 64π
2
cm
Exponents are often used in volume
problems to show the units are cubed
Volume = (length)(width)(height)
Length = 10 cm
Width = 10 cm
Height = 20 cm
20
10
10
3
Volume = (20cm)(10cm)(10cm) = 2,000 cm
What is the exponent?
(5)(5)(5)(5) = 5
4
What is the answer?
5
3
= 125
What is the base and the exponent?
(7)(7)(7)(7)(7) = 7
5
What is the base and the exponent?
(x)(x)(x)(x)(x)(x) = x
6
What the base and the exponent?
3 2
(a)(a)(a)(b)(b)(c) = a b c
Compute:
2
(-4)
Answer: (-4)(-4) = 16
PEMDAS
Calculate:
2
-4
Answer: -(4)(4) = -16
2
n
when n = -5
2
(-5)
= (-5)(-5) = 25
Simplify:
Answer:
Simplify:
Answer:
2
-n
2
-(-5)
when n = -5
= -(-5)(-5) = -25
Compute:
2
(-6)
Answer: (-6)(-6) = 36
Compute:
2
-6
Answer: -(6)(6) = -36
Compute:
2
-(-6)
Answer: -(-6)(-6) = -36
Simplify: (x +
2
3)
Answer: (x + 3)(x + 3)
2
x + 6x + 9
Compute:
2
0
Answer: (0)(0) = 0
Compute:
0
2
Answer: 1
Yes, it’s 1…explanation will follow
WHY is anything to the power zero "1"
6
3
= 729
35 = 243
4
3 = 81
3
3 = 27
32 = 9
1
3 =3
0
3
=1
Laws of Exponents
1. x  1
0
2. x
3. x  x  x
m
n
m n
5.  xy  x y
m
m
m
x
mn
7. n  x
x
n
1
1
n
 n or  n  x
x
x
 
4. x
m n
m
m
x
mn
x
x
6.    m
y
 y
m
A monomial is an algebraic expression
consisting of only one term.
 A term may be a number, a variable, or a
product or quotient of numbers and variables
(separated by a + or –)

Open Ended: Write 3 different examples
of monomials

Examples of monomials: 3, s, 3s, 3sp, 3s2p
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.) 3ab5
3.) Yes, this expression is a product of a coefficient and variables.
4.) j
4.) Yes, single variables are monomials.
Zero Exponent Property (1)
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
0
2.)  b   1
c
0
3.)  2   1
7
Open Ended: Create a problem
that satisfies this property!
Let’s practice
Simplify each expression:
1.
2.
3.
4.
5.
(-4)0
-40 (Recall PEMDAS - Exponents first!)
(5x)0 5x0
-(-4.9)0 (Recall PEMDAS – Exponents first!)
[(3x4y7z12)5 (–5x9y3z4)2]0
SWBAT… compute problems involving zero & negative exponents
Wed, 4/6
Agenda
1.
2.
3.
Review problems Zero & Negative Exponent Property (20 min)
Practice – hw#1 (15 min)
Quiz (10 min)
WARM-UP
1. (5x)0
2. 5x0
3.  Sophia ( Papaefthimiou ) 0
3
4.
(2)
HW: Quiz corrections
Agenda
1.
2.
3.
Lesson on monomials and exponents w/ many examples (20 min)

Zero Exponent Property

Negative Exponent Property
Practice – hw#1 (15 min)
Quiz (10 min)
WARM-UP
1. (5x)0
2. 5x0
3.(Teacher)0
HW: workbook p.187 and 195
Negative Exponent Property (2)
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,
a
n
1
1
n
 n and  n  a
a
a
Examples:
5
2
1
1
 2 
5
25
Open Ended: Create a problem that
satisfies this property!
Use any number for a and n.
1
3
m
3
m
12
8
1
4

Examples
1
12
1
1
 4 
4096
8
1
5

32
5
2

2
1
2

16
2  4
4
1
1
1
3 



3
(2)
( 2)
(2)( 2)( 2)
8
Examples (cont’d)
2
8 1
  2
1 2
9(6)
 9(1)
8 2
0
4 1
4
  2
2
1 4
4
2
2
8 1
 
1 4
2
9
 44
2
 416
2
1
2
1
1
2


  64
2  2  8
2
1 8
8
2
4
 64
 16
8 2
4
2
4
2
2
2
7
6
x y
0
2