7.2 Properties of Rational Exponents 7.2 Properties of Rational
Exponents
Algebra 2
Mrs. Spitz
Spring 2009
Objectives/Assignment
Use properties of rational exponents to
evaluate and simplify expressions.
 Use properties of rational exponents to
solve real-life problems, such as finding
the surface area of a mammal.

Assignment: pp. 411-412 #5-81 every 3rd
Review of Properties of Exponents
from section 6.1
am * an = am+n
 (am)n = amn
 (ab)m = ambm
1
-m
a = a
a
 a = am-n
a
a
   =
b

m
m
n
m
 
m
bm
These all work
for fraction
exponents as
well as integer
exponents.
61/2 * 61/3
= 61/2 + 1/3
= 63/6 + 2/6
= 65/6
b. (271/3 * 61/4)2
= (271/3)2 * (61/4)2
= (3)2 * 62/4
= 9 * 61/2
a.
(43 * 23)-1/3
= (43)-1/3 * (23)-1/3
= 4-1 * 2-1
c.
=&frac14;
*&frac12;
= 1/ 8
1 3

d. 18 4 
 1 
 94 


=
18
9
3
4
3
4
=
 18 
 
9
3
4
=
2
3
4
** All of these examples were in rational exponent form to begin with, so the
answers should be in the same form!
Ex: Simplify.
3
25

5=
a.
3
3
Ex: Write the expression in
simplest form.
25 5
3
a.
= 125 = 5
4
64
4
=
16  4
=
4
16  4 4
= 24 4
3
32
3
4
b.
=
3
=
3
32
4
b.
4
7
8
8 = 2
4
=
** If the problem is
begin with, the
=
4
4
7
8
7 42
4
8
2
4
=
4
14

2
Can’t have a tent in
the basement!
4
=
14
4
16
Ex: Perform the indicated operation
a.
5(43/4) – 3(43/4)
= 2(43/4)
b. 3 81  3 3
= 3 27  3  3 3
= 33 3  3 3
= 23 3
c. 3 625  3 5
= 3 125  5  3 5
3
3
= 5 5 5
3
=6 5
If the original problem is in radical form,
If the problem is in rational exponent form, the
answer should be in rational exponent form.
More Examples
x2  x
a.
b.
c.
d.
6
x 
x
11
y11 
y
4
6
r8 
4
r4 r4  4 r 4  4 r 4
 r r  r 2
Ex: Simplify the Expression.
Assume all variables are positive.
a. 27z  27  z  3z
3
9
3
3
(16g4h2)1/2
= 161/2g4/2h2/2
= 4g2h
b.
c.
5
x5
y10


x
y2
5
5
x5
y10
9
3
d.
18rs
2
3
1
4 3
6r t
 3r
3
4
1
2
3 3
3r s t
1
4
2
3
s t3
Ex: Write the expression in simplest
form. Assume all variables are positive.
4
4 9
a. 12d e f
14
 12  d  e  f
4
4
4
 12  d  e
4
 de 2 f
b.
5
34
9
4
24
e f
12ef
4
34
14
f
2
2
2
3
2 3
g2
g
h
g

h
5
5

10
h 7  h7  h3 
h
5
g 2 h3
h2
No tents in the basement!
3
2
3
c. 15d e f
 3d
4
5df
2
31 3
e f
1( 4 )
2
2 3
 3d e f 5
** Remember, solutions must be in the same form as the
original problem (radical form or rational exponent form)!!
8
d.
4
x y
6
z
11
4
8
11 2
x y z
6 2
z z
Can’t have a tent in the basement!!

8
4
11 2
x y z
8
z

2
x y
24
z
3 2
y z
2
Ex: Perform the indicated operation.
Assume all variables are positive.
a.
8 x 3 x  5 x
1
4
b. 3gh  6 gh
1
4
 3gh
c. 2 6 x  x 4 6 x
4
5
1
4
 2x 6x  x 6x
4
4
 3x 4 6 x
d.
6 s  2 s  s  6  2  1 s  5 s
e.
3 6y  2y
7
3
 3y
23
 5y
23
6y  2y
23
6y
6y
23
6y