Download Section 1.4 pp

Section 1.4
Positive Integer Exponents
Objectives: Use the properties of exponents
This section is prepared by M. Zalzali
Repeated Form and Exponent form
Exponents are used as a short-hand form for repeated multiplication.
Instead of writing
aaaaa
We write
a
Repeated Form
5
Exponent Form
Note “a” has been repeated 5 times, that’s why we wrote
a
5
a5 is read “ a to the fifth power’
a = Base, 5 = Power,
Example 1
Fill out the table with the correct answer
Repeated Form
7777
bbbbbb
(2x)(2x)(2x)
3 x  1
2
(2x+9)(2x+9)(2x+9)
Exponent Form
7
4
b6
2 x 3
(3x-1)(3x-1)
2 x  93
Rules and Properties of
Positive Integer Exponents
For any real number a and natural numbers m and n.
a a  a
m
First property
n
m n
Simplify each expression. ( Write in exponent form )
Example 1
i ) 10 10 
5
2
10
ii )  3  3 
5
15
iii ) 6b  6b   6b 
2
7
 3
20
7
5
iv )  xy xy 
xy
2
…
Simplifying Expressions
Note: When we multiply two expressions, we have to take into consideration the associative and
commutative properties of multiplication when needed.
Simplify the product
Example 2
2 x 5  6 x 2  2  6  x5  x 2  12 x 5 2  12x 7
Simplify the product
Class Exercise
6
15x
i) 5 x 3x  
3 4
2
3
ii ) 4a b 5ab  20a b
4
2
iv ) 2 x 3x   6x 2



iii ) 2c d 12cd  24c d
2
3
3
3
6
…
For any real number a , a  0,and natural numbers m and n.
m>n
m
Second Property
Example 3
a
mn
a
n
a
Simplify the expressions
x5
3
a  2  x
x
y14
c  5 
y
y
9
3 5
 35a 8b 6

25
m
n
4
5 2
5mn
b  3 4   5a b d 

2
7a b
 5m n
…
For any real number a and natural numbers m and n.
a 
m n
Third Property
Example 4
a
Simplify the expressions
a  x   x  x
16
2 8
b  a   a
6
2 3
c  10   10
3 5
35
15
mn
…
For any real number a and b , and natural number m
ab
m
Fourth Property
Example 5
a b
m m
Simplify the expressions
(a)  xy5  x 5 y 5
4


10
a
 10 4 a 4
(b)
(c)
2 p
2
q

3 3
3
  q 
 2 p
2 3
3 3
6
 8p q
9
…
For any real number a and b,
b0
and natural number m
m
am
a
   m
b
b
Fifth Property
Example 6
(a)  x 
2
Simplify the expressions
3
  
 y 
x 
2 3
6
x
 3
3
y
y
4
4 4
16
a
2
a
(b)  2a   4 
4
3
b
b
b 
4
…
Simplify the expressions
Class Exercise
Answers :
3
 5x 
a   2  
y 
  2a b
b  
5
c

3
4
2

 

a 
125 x 3
y6
b 
4a 6b 8
c10
…
For any real number a , a  0
a 1
0
Zero Exponent
Example 7
Simplify the expressions
a  10
0
 1
b  6x  61  6
2 3 0
c  a b   1
0
Home Work
Do the selected exercises from the syllabus
Section 1.4
The end