Section 4-1 Exponents
x3
x2
•
x•x•x
•
x 
3 2
=
(x • x • x)
x • x = x5
Name:
=
• ( x • x • x ) = x6
y 2 x 3 z 5
y 2 x 3 z 5
y4 y2 z5


y 4 x 6 z 7 y 4
x6 z 7 x3 x6 z7
x7 x x x x  x x x

 x3
x x x x
x4
=
y y y y  y y zzzzz
x x x  xxx x x x z z z z z zz
2
5
y6
x2  x 5
x9  z 2
1. Simplify
a. (5x
d.
2
5x
)(14x3)
3

y 2  6x 6 y 4
b.

e.
12 x 4 y 9
5
3x y
7
(-3m 3 n 4 ) 2 (4m 4 n 7 )
c.
3x
f.
24 a - 3 b 7 c 2
16 a 2 b 4 c 7
3
y2

2
(1 continued) Simplify
 3a 6 b 3c 2 

g. 
2 4 
 2a b 
2
j.
 4m 4 n -3 p 2
m. 
2 2
 6m n



h.
3x y z 4x y
k.
8 x y 3x
2
7
4
3
3
4
2 8
y8
z

2
2
n.

3 2 5 2
i.
5a b
l.
(9a3b5)(– 4a3b7)2
c

PROBLEM
CALCULATOR
73
7
,
^
2nd , x2
225
,
DIRECTIONS
3
, ENTER
, 2 , 2 , 5
, ENTER
X
4
4 ,
625
625
1
4
2
6 , 2 , 5
3 2
3
,
nd
,
^
, 6 , 2 , 5 , ENTER
,
^
,
(
^
,
(
, (-) , 2 , ) , ENTER
, 1 ,  , 4 , ) , ENTER
2. Evaluate the following.
a.
5
243
b.
4
2401
c. 243
1
5
d. 2401
1
4
e.

 243
32 
2
5
3. Rewrite the following using fractional exponents and simplify when possible:
a.
6
x4  3 x6
b.
a
5
3
c.
4b 
2 3
d. 5 243 x 25 y 12 z  8
4. Rewrite the following using radical form.
a.
8
3
5
x3
b. a 2
c. 8 3

d. 81
3
4
5. Simplify the following (write the solutions using a rational exponent).
5
6
y y
a.
1
4
b.
x
x
 25

c. 81  x 4
 11
5

3
4
2

1
3
d. a  a
1
1
6

4
5
3
 m4
e.  1
 m2

1
x4  x6
g.
x
1
3
b.
x
x
3
3



f.
6
h2  3 h
**Hint: rewrite in rational
exponent form first.**
3
c.
4
p
5
p2  3 p
**Hint: rewrite in rational
exponent form first.**
**Hint: rewrite in rational
exponent form first.**