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Exponents
Section 1.4
Properties Review
• Product of Powers
a ×a = a
m
n
m+n
m
• Quotient of Powers
a
mn

a
n
a
• Power of a Power
(a ) = a
• Power of a Product
(ab) = a b
• Power of a Quotient
m n
m
m
mn
m m
m
a
æ aö
çè ÷ø = m
b
b
Examples
1.) 3 x  5 x
4
4 3
2.) ( 3 xy z )
5
3 2 3
2 2
3.) (2 x ) (3 xy )
25 x
4.)
5x
3
Examples
 a 
6.)  6 2 
a b 
2
4
12a b
5.)
3
2a b
2
7.)  5 x y z
3
5
 2x y 
8.)  2 4 
 5x y 
3
3
2
Zero Power
Any number (except zero) raised to the zero
power is equal to 1.
Definition of Rational Exponents
• For all positive real numbers a:
– If n is a nonzero integer, then:
1
n
a =na
– If m and n are integers and n ¹ 0 then:
m
n
1
n m
a = (a ) = ( a ) = a
n
m
n
m
Review:
2
36 = 6
100 =10
2
9 =3
3
27 = 3
3
8 =2
Examples
1
4
16 = 16 = 2
4
4
3
3
3
2
2
27 = ( 27 ) = (3) = 81
4
4
36 = ( 36 ) = (6) = 216
3
3
Try This:
2
3
1.) 64
3
2
2.) 81
3.) 8
2
6
Try This:
4.)  8
2
3
5.) (8)
6.) 4

5
2
2
3
Assignments
• First day - Pg. 99 #19-58 all
• Second day - Pg. 99 #59-69 odd