Transcript 5.4 Exponent Rules and Multiplying Monomials 1. Multiply monomials. 2. Multiply numbers in scientific notation. 3.

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   4
2
 3  3
6
 48
4
 48
5
 39
 39
3
5
8
2a  7a  14a
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
2x 5x 
3 an equation
3 in one variable is solved the answer3is a point on3a line.
When
2x  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 a3  64a 3
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
2x 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
4 2
x y
 x 15 y 10
Simplify:
2x y 2xy 
2
4
23
3x4 y2z yz 4 
2 4 x 8 y 4 23 x 3 y 6
27 x 11y 10  128x 11y 10
When an equation
point6on3a line
5 . 20
3 in one 5variable is solved the answer 3is a12
3 x y z y z
33 x 12 y 11 z 23  27x 12 y 11 z 23
 x y   x y 
5 2 3

2 32

 x 15y 6 x 4 y 6
 x 19 y 12
Simplify.  6b
7
 3b 
3
a) 18b 21
b) 18b10
c) 9b21
d) 9b10
5.4
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Slide 5- 17
Simplify.  6b
7
 3b 
3
a) 18b 21
b) 18b10
c) 9b21
d) 9b10
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 18
Simplify.  4 y
2
 5 y 
3 4
a) 20y 9
b) 20y20
c) 2500y9
d) 2500y14
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 19
Simplify.  4 y
2
 5 y 
3 4
a) 20y 9
b) 20y20
c) 2500y9
d) 2500y14
5.4
Copyright © 2011 Pearson Education, Inc.
Slide 5- 20