Transcript 7.1 Multiplying Monomials Monomial

Monomial - a number, a variable or a
product of a number and one or more
variables.
Examples :
7 , y , 3 a , 4 xy
Monomials do not have variables in the
denominator.
A real number is a monomial called a constant.
Example 1 – Determine whether the
following expressions are monomials.
a. 10
yes, this is an example of a constant
b. x + y no, this expression involves the
addition not the product of
variables
c. x
yes, a single variable is a monomial
d.
3
x
no, cannot have variables in the
denominator
Fill out Frayer Model with your partner
Definition
Characteristics
Monomials
Examples
Non-examples
Homework p. 361 14-19
7.1 Multiplying Monomials (Day 2)
A number or variable with an exponent is called
a power.
3
2
3 is the base; 2 is the exponent
x
3
x is the base; 3 is the exponent
The exponent tells you how many times to use
the base as a factor.
x
3
 xxx
Rules of Exponents:
1. Product of Powers: when multiplying powers
with like bases add exponents.
x x  x
2
3
23
or x
5
Example 1 – Simplify
3 x y  x
2
4
y
3

Group coefficients
( 3 x y )( x y )  ( 3 )(1)( x )( x )( y )( y ) and variables
2
4
3
2
 ( 3  1)( x
 3x y
6
4
2 4
4
)( y
3
1 3
)
Product of Powers
Simplify
Try - Simplify:
7
5
3
6
( 4 x y )( 6 x y )
 ( 4 )( 6 )( x )( x )( y )( y )
7
 ( 4  6 )( x
 24 x y
10
73
11
3
)( y
5
5 6
)
6
Rules of Exponents:
2. Power of a Power: to find the power of a
power multiply exponents.
(x )  x
2 3
2 3
or x
6
Example 2 – Simplify
2
3 2
[( 2 ) ]
 (2
2 3
 (2 )
 (2
)
6
2
6 2
)
 2
12
 4 , 096
2
Try
2
4 2
[( 3 ) ]
 (3
2 4 2
3
16
)
 43 , 046 , 721
Rules of Exponents:
3. Power of a Product: to find the power of a
product find the power of each factor and
multiply.
( 3 xy )  ( 3 ) x y or 27 x y
3
3
3
3
3
3
Example 3 – Simplify
( 5 ab )
3
 (5) a b
3
3
 125 a b
3
3
3
Try
( 4 xy )
2
 (4) x y
2
2
 16 x y
2
2
2
Homework:
Page 361 20 - 28
7.1 Multiplying Monomials Day 3
Simplifying Monomial Expressions:
Each base appears exactly once,
There are no powers of powers, and
All fractions are in simplest form
Example 1: Simplify
[( 8 g h ) ] (  2 gh )
3
4
2 2
5
4
 (8 g h ) (  2 gh )
3
4
4
5
4
 (8 ) ( g ) ( h ) (  2 ) g ( h )
4
3
4
4
4
4
4
 ( 4 , 096 ) g h (16 ) g h
12
16
4
 ( 4096 )(16 ) g g h h
12
 65 ,536 g h
16
36
4
16
20
5
20
4
Try:
(  2 v w ) (  3 vw )
3
4
3
3
2
 (  2 ) ( v ) ( w ) (  3) v ( w )
3
3
3
4
3
2
  8 v w (9 ) v w
6
 (  8 )( 9 ) v v w w
6
9
12
2
9
2
  72 v w
18
11
12
2
3
2
Do the online Self-Check Quiz for 7.1 with your
partner.
When you complete the quiz click the “check
it” button. Fill in the boxes to e-mail results.
Your Name: partner’s names
Your E-mail Address: Algebra
E-mail results to:
[email protected]
Homework:
Page 362 31 – 34, 39 & 40