Download Lesson08 - Purdue Math

Lesson 8 Notes Sections 1.6
Rules of Exponents
A
Product and Quotient Rules
Product Rule:
a m a n  a mn
Quotient Rule:
am
 a mn
n
a
Product Rule
1.
2.
Keep Base
Add exponents
1.
Keep Base
2.
Subtract exponents
(numerator - denominator)
Examples:
1)
9 4  93  9 2 
2)
m 3 m 2 m 5 
3)
(5a 2 )( 2a 3 )( a) 
4)
( xy 2 )(2 x 2 y)( x 5 y)(3 y 2 ) 
5)
48

46
7)
 8x 5 y 3 z 2

2 x 2 yz
Caution:
and
Quotient Rule
6)
n11r 2

n5r
a m a n  (a  a) mn  58  5 2  2510
am
56
m/n
a
 2  53
n
a
5
1
B
Zero and Negative Exponent Rules
Zero Exponent:
Negative Exponent:
a0  1
a
n
a
1
1
 n , n  a n ,  
a a
b
n
b
 
a
n
Examples:
1)
20 
3)
 2x 0 
4)
(2 xy0 )(3 y 2 ) 
5)
a5

a7
7)
9)
(2 3 )(2) 
2)
6)
8)
(mn) 0 
mn0 
x5 y

3 5
x y
m 2

m 5 n
r 5 t 2 v 1

r  4 t 3 v 3
Caution: A negative number does not necessarily mean a negative number. Think
reciprocal when you see a negative exponent, not negative number.
2
C
Power Rules
n
(a )  a
m n
mn
(ab)  a b
n
n
n
an
a
   n
b
b
Note: Power Rules are used top remove or clear parentheses.
Examples:
1)
(2 5 ) 2 
3)
(3x 2 y) 3 
4)
 4x 2
 3
y
5)
(5 x 2 y 3 ) 2 
D
1.
2.
3.
4.
5.
2)
(ab) 5 
3

 

Putting all the Rules together....
The rules can be performed in many different orders when simplifying
expressions. However, if you do not know what order to use, these steps usually
work well.
Simplify within parentheses first using product or quotient rules and/or
negative or zero rules.
Clear parentheses by using power rules.
Change any zero or negative exponent rules.
Continue with product or quotient rules, if necessary.
Evaluate or simplify any numbers, if needed.
3
Examples:



2
1)
 2 x 2 y 2

5
 3x
2)
 3 p 2 p 3 

 
5
p


3)
(8x 2 y 3 ) 2 ( x 3 y) 3 ( xy 2 ) 
4)
(2a 2 b 1c) 3

a 2 b 2 c 1

2
4