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
Examples
Monomials
Non-examples

Homework p. 361 14-19

7.1 Multiplying Monomials (Day 2)
A number or variable with an exponent is called a power.
2
3 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
2  x
3  x
2

3 or x
5

Example 1 – Simplify
( 3 x
2 y )( x
4 y
3
)

( 3 )( 1 )( x
2
)( x
4
)( y )( y
3
)

( 3

1 )( x
2

4
)( y
1

3
)
 x
6
3 y
4
Group coefficients and variables
Product of Powers
Simplify

Try - Simplify:
( 4 x
7 y
5
)( 6 x
3 y
6
)


( 4 )( 6 )( x
7
)( x
3
)( y
5
)( y
6
)
( 4

6 )( x
7

3
)( y
5

6
)
 x
10
24 y
11

Rules of Exponents:
2. Power of a Power : to find the power of a power multiply exponents.
( x
2
)
3  x
2

3 or x
6

Example 2 – Simplify
[( 2
2
)
3
]
2

( 2
2

3
)
2

( 2
6
)
2

( 2
6

2
)


2
12
4 , 096

Try
[( 3
2
)
4
]
2

( 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 
( 3 )
3 x
3 y
3 or 27 x
3 y
3

Example 3 – Simplify
( 5 ab )
3

5 )
3 a
3
( b
3
 a
3
125 b
3

Try
( 4 xy )
2

( 4 )
2 x
2 y
2
 x
2
16 y
2

Homework:
Page 361 20 - 28

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
3 h
4
)
2
]
2
(

2 gh
5
)
4

( 8 g
3 h
4
)
4
(

2 gh
5
)
4

( 8 )
4
( g
3
)
4
( h
4
)
4
(

2 )
4 g
4
( h
5
)
4

( 4 , 096 ) g
12 h
16
( 16 ) g
4 h
20

( 4096 )( 16 ) g
12 g
4 h
16 h
20

65 , 536 g
16 h
36

Try:
(

2 v
3 w
4
)
3
(

3 vw
3
)
2

(

2 )
3
( v
3
)
3
( w
4
)
3
(

3 )
2 v
2
( w
3
)
2
 
8 v
9 w
12
( 9 ) v
2 w
6

(

8 )( 9 ) v
9 v
2 w
12 w
6
  v
11
72 w
18

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: vomastekla@southfield.k12.mi.us

Homework:
Page 362 31 – 34, 39 & 40