# 6-2

```6.2A Apply Properties of
Rational Exponents
Algebra II
Review of Properties of Exponents
from section 5.1
am * an = am+n
 (am)n = amn
 (ab)m = ambm
These all work
 a-m = 1
a
a
for rational
 a = am-n
(fraction)
a
a


   =
exponents as
b
b
well as integer
exponents.

m
m
n
m
m
m
Ex. 1 : Simplify. (no decimal answers)
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 2: Simplify.
3
25

5=
a.
3
3
Ex 3: 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 4: 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.
6.2B Simplifying Expressions with
Variables
Ex. 1
x2  x
a.
b.
c.
d.
6
x 
11
y13 
4
7
r8 
4
x
6
y
11
x
y
2
r4 r4  4 r 4  4 r 4
 r r  r 2
Ex 2: 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. 3 Perform the indicated operation.
Assume all variables are positive.
a.)18 u  11 u
3
3
4 2/3
b.)15a b
 8a b
4 2/3
c.)10 5s  3s 80 s
4
7
4
3
Assignment
Ex. 4 Write the expression in
simplest form.
3
a.) 104
4
10
b.) 4
27
```