Download Section 5.4

5.4
Exponent Rules and Multiplying
Monomials
1. Multiply monomials.
2. Multiply numbers in scientific notation.
3. Simplify a monomial raised to a power.
Objective 1
Multiply monomials.
23 • 2 4
23 means
three 2s.
23

 222


27
24
2222
24 means
four 2s.
Since there are a total of seven 2s multiplied,
we can express the product as 27.
Keep the base and add the exponents
Product Rule for Exponents
If a is a real number and m and n are integers,
then am • an = am+n.
Multiply:
2
9 9
5
4
6
3 3
97
310
When an equation in one variable is solved the answer is a point on a line.
 4 2   4 6
 4 8
 3  3
4
 48
5
 39  39
3
5
2a  7a  14a
8
Multiplying Monomials
1. Multiply coefficients.
2. Add the exponents of the like bases.
3. Write any unlike variable bases unchanged in
the product.
Simplify:
3
5x  7 x
2
2
4
5 3
35x
25  81  2025
5
2x3 5x3 
3 a line.
When an equation in one variable is solved the answer3is a point on
2 x  5x
10x
6
 1 2  5
3  2 5 
  k m  km n   k 
 4
 6
 3 
7x 3
5 8 4
k m n
36
Objective 2
Multiply numbers in scientific
notation.
Monomials:
Scientific notation:
4a3 2a6   4  2a36
3
6
3 6
4

10
2

10

4

2

10



 8a9
 8 109
Multiply and write result in scientific notation:
3
4
4.5

10
5.7

10



25.65  107
2.565  108
When an equation in one variable is solved the answer is a point on a line.
3
6
6.2

10
3.1

10



19.22  10 3
1.922  10 2
Objective 3
Simplify a monomial raised to a
power.
x 
2 5
2
2
2
2
 x x x x x
2
x
10
A Power Raised to a Power
If a is a real number and m and n are integers,
then (am)n = amn.
4a
3
 4a 4a 4a   4 3 a 3  64a3
Raising a Product to a Power
If a and b are real numbers and n is an integer,
then (ab)n = anbn.
2x y 
3 2 4
4 12 8
12 8
 2 x y  16x y
Simplifying a Monomial Raised to a Power
1. Evaluate the coefficient raised to that power.
2. Multiply each variable’s exponent by the power.
Simplify:
3x y 

2 32

2 3 5
2x y
2 x 10 y 15
9x 4 y 6
When an equation in one variable is solved the answer is a point on a line.
 x y
2
 x y 
2
3 2 5
x4y2
 x 15 y 10
Simplify:
2x y 2xy 
2
4
23
3x4y2z yz4 
2 4 x 8 y 4 23 x 3 y 6
27 x 11 y 10  128 x 11 y 10
When an equation
point6on3a line
5 . 20
3 in one 5variable is solved the answer 3is a 12
3 x y z y z
33 x 12 y 11 z 23  27 x 12 y 11 z 23
 x y   x y 
5 23

2 32

 x 15 y 6 x 4 y 6
 x 19 y 12
7
3
6
b
3
b
Simplify.   
a) 18b 21
b) 18b10
c) 9b 21
d) 9b10
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 17
7
3
6
b
3
b
Simplify.   
a) 18b 21
b) 18b10
c) 9b 21
d) 9b10
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 18
Simplify.  4 y
2
5 y 
3 4
a) 20 y 9
b) 20 y 20
c) 2500 y 9
d) 2500y14
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 19
Simplify.  4 y
2
5 y 
3 4
a) 20 y 9
b) 20 y 20
c) 2500 y 9
d) 2500y14
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 20