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Document related concepts
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Transcript 
a a
m
 ab 
n
m


a
mn
m
a b
m
a a
m
 ab 
n
m
a 
n
m

a
mn
m

a b

mn
a
m
a
 
b
m
m

b0
a
m
b
m
a
n
a

a0
a
mn
m
a
n
a

a
mn
mn
m
a
m
a

1
m
a
m
a

1
m
a
m
a

a
mm

a
0
m
a
m
a

1
m
a
m
a

a
mm

a
0
a
0

1
m
a
n
a
nm
1
a3
2
a
5
a
1

3
a
1
2
a
5
a
1

3
a
a3
2
a
5
a

a
2 5

a
3
2
a
5
a
1

3
a
2
a
5
a

a
2 5

a
3
a
n

1
n
a
 2
2
 2
2
 2
2
2
 2
2
2
Let 2  2
x
 2
2
2
Let 2  2
x
2 
2
x
2
2 
2
x
2
2   2
2
x
1
2   2
2
x
2
2x
1
2
1
2   2
2
x
2
2x
1
2
1
2   2
2
x
2
2x
1
2
2x  1
1
2x  1
1
x2
1
x2
22
x
22
1
2
n
a
1
n
a
3
4
16
3
4
16
 2
2
4 3
4
2
3
4
16
8

3
4 4
3
2  16
4
a 
m n
a
multiply
mn
125
2
3
 5
3

 23
 
3  23
5
2
5
 12
5
125
2
3  1
25
53  125
a 
m n
a
multiply
a
n

1
an
mn
1) 169
3) 36
1
2
 12
2)  27 
4) 16
2
3
 14
Final answer written without negative exponents
1) 13
3)
1
6
2)
4)
9
1
2
3
64
2
3
64
2
  64
 64
2 1
3
 64
2
3
 2

1
2 3
n
a
a 
m n
1
an
a
mn
multiply

2
6 3
2  64
6
 2
2
6 2
3
2
3
64
2

2
6 3
4
 16
a 
m n
a
multiply
mn
5)
7)
3
216
1
100
5
2
6)
8)
4
3
625
1
7
128
4
Final answer written without negative exponents
5)
 36
7)
1
100, 000
6) 125
8)
1

16

4
7
2x y
1
5

2
7
5x y
4
5

 2 x y 5x y 
  2  5   x  x  y  y 
4
7
1
5
2
7
4
7
2
7
4
5
1
5
4
5
Commutative
Associative
 2 x y 5x y 
  2  5   x  x  y  y 
4
7
1
5
2
7
4
7
2
7
4
5
1
5
4
5
Commutative
Associative
 2 x y 5x y 
  2  5   x  x  y  y 
4
7
1
5
2
7
4
7
2
7
4
5
1
5
4
5
Commutative
Associative
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
4
7
1
5
2
7
4
7
42
7 7
4
5
2
7
1
5
14
5 5
4
5
Commutative
Associative
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
4
7
1
5
2
7
4
7
42
7 7
4
5
2
7
1
5
14
5 5
4
5
Commutative
Associative
a a a
m
n
mn
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
4
7
1
5
2
7
4
7
42
7 7
4
5
2
7
1
5
14
5 5
4
5
Commutative
Associative
a a a
m
n
mn
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
 10   x   y 
4
7
1
5
2
7
4
7
4
5
2
7
1
5
42
7 7
6
7
14
5 5
5
5
4
5
Commutative
Associative
a a a
m
n
Add
mn
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
 10   x   y 
4
7
1
5
2
7
4
7
4
5
2
7
1
5
42
7 7
6
7
14
5 5
5
5
4
5
Commutative
Associative
a a a
m
n
Add
mn
 2 x y 5x y 
  2  5   x  x  y  y 
 10   x  y 
 10   x   y 
4
7
1
5
2
7
4
7
4
5
2
7
1
5
42
7 7
6
7
6
7
 10x y
14
5 5
5
5
4
5
Commutative
Associative
a a a
m
n
Add
mn
 4x
2
y

1
4 2
4
1
2
 
x
1
2 2
y

1
4 2
 ab 
m
 a b
m
m
 4x
2
y

1
4 2
4
1
2
 
x
1
2 2
y

1
4 2
 ab 
m
 a b
m
m
 4x
2
y

1
4 2
4
1
2
 
x
1
2 2
y

1
4 2
 ab 
m
 a b
m
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2
1
2 2
x
y
2 12

1
4 2
y
4 12
 ab 
m
 a b
m
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2
1
2 2
x
y
2 12

1
4 2
y
4 12
 ab 
m
 a b
a 
m n
m
a
mn
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2
1
2 2
x
y
2 12

1
4 2
y
4 12
 ab 
m
 a b
a 
m n
m
a
mn
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2 2
1
2
x
2 12
2 x y
1
1
y
2

1
4 2
y
4 12
 ab 
m
 a b
m
a 
a
a
 a mn
m n

m n
mn
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2 2
1
2
x
2 12
2 x y
1
1
y
2

1
4 2
y
4 12
 ab 
m
 a b
a 
m n
m
a
Multiply
mn
m
 4x
2
y

1
4 2
4
1
2
 2
2
 
x

1
2 2
1
2
x
2 12
2 x y
1
1
y
2

1
4 2
y
4 12
 ab 
m
 a b
a 
m n
m
a
Multiply
mn
m
 4x
2
y

1
4 2
4
1
2
 2
 
2
x

1
2 2
1
2
x
2 12
2 x y
1
2x
 2
y
1
y

1
4 2
y
4 12
2
1
y  2
y
2
 ab 
m
 a b
a 
m n
m
a
Multiply
mn
m
 4x
2
y

1
4 2
4
1
2
 2
 
2
x

1
2 2
1
2
x
2 12
2 x y
1
 4x
2
y

1
4 2
2x
 2
y
1
y
2

1
4 2
y
4 12
 ab 
m
 a b
a 
m n
m
a
Multiply
mn
m

1
3
9) 2 x y
1
2
3x y 
2
3
 8x y 
11)  3 
 z

3
6
1
3
1
2
10)  64x y z
3
6 1
y z 
12) 
5 
 32 x 
5 10

1
3
 15
Final answer written without negative exponents
9)
6xy
10)
4 xy
z
11)
2 xz
2
y
12)
1
3
2 xy
2
z
2
4 3
12
x y
36


3
12
x y
36

1
4
n
a
1
an
4 3
12
x y
36


3
12
x y
36

1
4
n
a
1
an
4 3
12
x y
36


3
12
x y

12
 x y

36


1
4
1
36 3
n



1
4
a
1
an
4 3
12
x y
36


3
12
x y

36
1
4

12
 x y

1
36 3
 x y

12

1 1
36 3 4
n



a
1
an
1
4
a 
m n
a
mn
4 3
12
x y
36


3
12
x y

36
1
4

12
 x y

1
36 3
 x y

12

1 1
36 3 4
n



a
1
an
1
4
a 
m n
a
mn
 x y

12
1
36 12
1
1212
1
3612
x
y
a 
m n
a
mn
 x y

12
1
36 12
1
1212
1
3612
x
y
a 
m n
a
mn
 x y

12
1
36 12
1
1212
1
3612
x
x y
1
3
y
a 
m n
a
mn
 x y

12
1
36 12
1
1212
1
3612
x
x y
1
3
y
a 
m n
a
mn
 x y
1
1212
1
3612
x
4 3
12
x y
36

12
1
36 12
x y
1
3
y
a 
m n
a
mn
Page 443
Practice Exercises
#13 - 14
Final answer written without negative exponents
13)
8
16
x y
8
14)
4
16x y
8
Final answer written without negative exponents
2
13)
x
y
14)
2x
2
y
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