Download I can multiply and divide monomial expressions with integer

I can multiply and
divide monomial
expressions with
integer exponents.
What are the properties of exponents? How do we use these properties to
simplify expressions?
Concept Attainment Activity
During this activity you will be given examples. Some of
the examples will demonstrate the concept accurately and
some will not. You will be told which is which, and your
job is to discover the pattern and correctly state the rule
for the property shown based on the pattern you have
seen.
Exponent
Properties
Involving
Products
Product of Powers
Is an Example
Is Not an Example
5 5  5
9
6 6  6
10
8
3  3  3
7 7  7
2
2
3
x x xx

2
12
6
9



3
y  y y  y
3
5
6
16
Product of Powers
Property
The rule:
a  a
m
n
a
m n
Power of a Power
Is an Example
Is Not an Example
4   4
2   2
9 
7
2
14
4 5
n
3

n
n 
5

20
m
1

m
1







5 4
7
5   5
18

9
3 4
20
6
4
3
2
n
7
25
a 1   a 1
3 2
9
Power of a Power
Property
The rule:
a 
m
n
a
mn
Power of a Product
Is an Example
5x   25x
2
3x   3x
2
2
23 17  23  17
5
5
3


2
42 12  42 144
2
5
4mn  64m n

3
Is Not an Example

9xy
2
3
 81xy
Power of a Product
Property
The rule:
ab  a  b
m
m
m
2 2 2
4
9
3
14
2

5 2
10
3
b  2 
b  2
2 6
12
7xy
2
2
49x y
6d  2d

xy z  x yz
2
5 4
2 3 5
4
2
96d
2
22
13 12 17
x y z
Exponent
Properties
Involving
Quotients
Quotient of Powers
Is an Example
11
6
6

6
5
6
4 
7

4
 
2
4 
48
11

4
43
9
9 9
5
9
2

9
4
Is Not an Example
5
6
5
3
 5
3

1 8
3
5 y  y
y

6
7
2
7
3
7
1 6
19
4 x  x
x
2
Quotient of Powers
Property
The rule:
m
a
m n

a
,a

0
n
a
Power of a Quotient
Is Not an Example
Is an Example
x 3 x 3
   3
y  y
2x 3 2x 3
  
y
 y 
 7 2 49
   2
 x  x
5x 2 25x 2
  
3y
3y 


Power of Quotient
Property
The rule:
a 
a
   m ,b  0
b 
b
m
m
3 4
 
4 
34
4
4
1
5
3
38
1 5
 
3 
1 4
   312
3 
3x 5 3

2 
7 y 
15
27x
6
343y
3x 3 2 1

  2
 2 y  x
2s 3 t 3

2
st
4
3st 
s2 t
3
9x
2
4y
3 3
54s t
Find the values of x and y if you know that
x
2
bx
9and b  b
13

b

b
by
b 3y
Explain your reasoning.

x = 8 and y = 1

Zero and Negative Exponents
4
3x3x3x3
81
3
3
3x3x3
27
3
2
3 xMath
3
1
3
3
3
3
is the9study of
patterns!

0
1
3
3
1
1
31
1
3
1
1
4  4 
3 3 81
3
2   1
  2 3
3   

3 


1  
3
4
1
1
43

2 3
1   
3 


1
1
64
3 3 27
1   
2 
8
1
64
1
 1
 64
64
1
5
 125

3 1
3  3
5
5
2
 1296
6
2
6
8 7
12x y
4 x
2
y
6
1
12

2
3x y

4
5
12x 8
12x 8
12x 8


2 
7


16y
 4 
16
7
7
y  2 6  y  4 12 
4 12
x y  x y
x y 
7
4 12
16y
8 x y
 12x  4 12  12x 
7
x y
16y
8
12 12
12x y

7
16y
12
3x y

4
5