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M098
Carson Elementary and Intermediate Algebra 3e
Section 5.4
Objectives
1.
2.
Multiply monomials
Simplify a monomial raised to a power.
Vocabulary
Prior Knowledge
If a is a real number except 0 and n is a natural number, then a  n 
1
If a is a real number except 0 and n is a natural number, then
a
n
1
an
.
 an .
Example 1:
a 2b 4
c 3

b 4c 3
a2
New Concepts
If a is a real number and m and n are integers, then am  an  am n .
Example 2:
a.
9 2  95  97
f.
52  34
(Can’t use the product rule. Evaluate.)
b.
34  36  310
g.
2x3  5x3  7x3 (Adding like terms)
h.
 2x3  5x3   10x 6



i.
 1 2  5
3  2 5 
  k m  km n   k  =
4
6


 3

b.
c.  42   46   48  4 8
(A negative number raised to an even
power is positive.)
 34   35   39  39
d.
(A negative number raised to an odd
power is negative.)
e.
V. Zabrocki 2011
5 8 4
k m n
36
5x 3  7x 2  35x 5
page 1
M098
Carson Elementary and Intermediate Algebra 3e
If a is a real number and m and n are integers, then  am 


n
Section 5.4
 amn .
Example 3:
a.
x 2 5  x 2  x 2  x 2  x 2  x 2  x10
c.
4a3  4a4a4a  43 a3  64a3
 m 4 


b.
b
3
 m12
If a and b are real numbers and n is an integer, then abn  anbn .
Example 4:
a.
 3x 2 y 3 


2
 3 2 x 2 2 y 3  2  9 x 4 y 6
b.
2 x 2 y 3 


5
 2x10 y15
e.
4
3
 2x 2 y   2xy 2   128x11y10

 

b.
f.
3
5
 3x 4 y 2 z   yz 4   27x12y11z 23

 

2
  x 2 y    12 x 22 y12  1x 4 y 2  x 4 y 2


(A negative number to an even power is positive.)
c.
d.
V. Zabrocki 2011
5
  x 3 y 2   x15 y10


g.
 x 5y 2 3  x 2y 3 2  x19y12
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