Download Document 8935036

M098
Carson Elementary and Intermediate Algebra 3e
Section 5.1
Objectives
1.
Evaluate exponential forms with integer exponents.
Vocabulary
Exponent
A symbol written to the upper right of a base number that indicates how many times to
use the base as a factor
The number in an exponential expression that is repeatedly multiplied.
Base
Prior Knowledge
Evaluating exponential expressions.
4
2 = 16
4
(-2) = 16
3
(-2) = -8
4
-2 = -16
3
-2 = -8
even power
(negative)
= positive
odd power
(negative)
= negative
4
the additive inverse of 2
3
the additive inverse of 2
New Concepts
Evaluate exponential forms with integer exponents.
Observe the following pattern:
3 4  81
1
1
 1
3
3
1
1

 2
9
3
1
1

 3
27
3
3 1 
3  27
3
32
32  9
31  3
33
30  1
0
If a is a real number except 0, then a = 1.
Example 1:
0
a.
5 =1
b.
(-5) = 1
c.
 1 
  1
 25 
d.
(6y) = 1
0
f.
-5 = -(1) = -1
g.
3 –4 =1–1=0
h.
(8w) (-6x ) (-2y) = (1)(-6x )(1) = -6x
i.
(3 – 3) = 0
0
0
0
0
e.
V. Zabrocki 2011
0
0
2
0
0
0
2
2
(?) Indeterminate
0
6y = 6(1) = 6
page 1
M098
Carson Elementary and Intermediate Algebra 3e
Section 5.1
If a is a real number except 0 and n is a natural number, then a  n 
1
an
.
Example 2:
1
a.
23 
b.
3x  2 
c.
 4x  3 
1
8

23
 5x 3 (no negative exponents)
d.
3
5
e.
x2
x 3
 5  x 3  5 
1
x3
 5
x3
 5x 3
1
4
x3
If a is a real number except 0 and n is a natural number, then
1
 an .
a n
Example 3:
a.
b.
2a 3
b2
a 2b 4
c 3


2
a 3b 2
b 4c 3
c.  3 3 x 2 y  3 
4h 5
d.
a2
m  2k
3
 
x
e.

4m 2
h5k
2

2
1
3
 
x
2
9
x2
x2
3
x
 1     1  2  1

 
x
9
9
x
 
3
2
 33 x 2
y3
a
If a and b are real numbers except 0 and n is a natural number, then  
b
n
n
b
  .
a
Example 4:
a.
V. Zabrocki 2011
p
 
 q
6
6
 q
q6
    6
p
p
b.
2
 
3
3
3
27
3
  
8
2
page 2