7.4 Rational Exponents
Objective:
Be able to simplify expressions with rational
(fraction) exponents
Chapter 7 Test Thursday/Friday!
Rational Exponents
Rational Exponent: Another way to write a radical expression.
Radical
Form
3
4
4 
Exponent
Form
1
42
8 
1
3
8
16 
1
16 4
Simplifying
Simplify each expression.
Ex1)
1
64 3
Ex2)
1
72
Ex3)
1
162 4
Ex4)
1
53
1
 72
1
 253
Definition
If the n th root of a is a real number and m is an integer,
1
n
m
n
then a  a and a  a 
Example :
n
2
36 3
 36
3
n
2
m
or
 a  . If m is negative, a  0.
n
m
2
36 3

*Which one is easier to find?
*It’s usually easier to take the root first!

3
36

2
Converting
Write the exponential expressions in radical form.
Ex5)
2
x7
Ex6) y 0.4
Write the radical expressions in exponential form.
Ex7) 4 c3
Ex8)
 c
5
Simplifying Numbers
Simplify each number.
Ex9)  27 
2
3
2.5
Ex10) 25
Ex11)  32 
4
5
What you got!?
Write is simplest form.
Ex12)

2
243a 10 5

Properties
Property
Example
a m  a n  a m n
m n
mn
a   a
ab   a b
m
a
m
m
1
 m
a
am
mn
a
n
a
m
a  a
 
m
b
b
m
m
Examples
Write each expression in simplest form.
Ex1)
3
16 y 8 4


Ex2)

1
8x15 3

Examples
 2
3x 3
Ex3) 





1
Ex4)

1
27x 9 3

1
x3  4

Ex5)  1 
x 
Examples
Ex6)
1
y2

3
y 10
Ex7)
5
y7

3
y 14
1
 81 y16  2
Ex8) 
12 
 16 x 
DUE AT END OF CLASS!
Page 389
#66, 68, 70, 74
7.4a Rational Exponents
Homework #10
Pg 388 #2-24 even, 30-48 even, 65-73 odd
Chapter 7 Test Thursday/Friday!