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Section 7.4 Notes: Rational Exponents
Example 1: Simplifying Expressions with Rational Exponents
Simplify each expression.
a) 125
1
3
1
2
b) 5  5
1
3
1
2
c) 10  100
1
3
Definition: If the nth root of a is a real number and m is an integer, then
1
m
a n  n a and a n  n a m  (n a ) m .
If m is negative, a  0 .
Example 2: Converting to and from Radical Form
Convert the expressions to the reciprocal form. Simplify if needed.
3
a) x 5
b)
c) y 2.5
a3
d) (5 b ) 2
Summary: Properties of Rational Exponents
am  an  amn
(a m )n  a mn
am 
3
(5 xy) 6
(ab)m  a mbm
am
 amn
n
a
1
am
e)
a
am
( )m  m
b
b
Example 4: Simplifying Numbers with Rational Exponents
3
a) (32) 5
b) 4 3.5
3
3
c) 32 5
d) 25 2
Example 5: Writing Expressions in Simplest Form
Write each expression in simplest form.
8
a) (16 y )

3
4
15
b) (8 x )

1
3
1
c) (243a
2
10 5
)
  1  2  3
d)  x 2  

 
