7.4a Rational Exponents
Seize the moment of excited curiosity on any subject to
solve your doubts; for if you let it pass, the desire may
never return, and you may remain in ignorance.
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

7.4a Rational Exponents
HW 7.4a: 1-37 all, omit #19-21, 25
Seize the moment of excited curiosity on any subject to
solve your doubts; for if you let it pass, the desire may
never return, and you may remain in ignorance.