Download alg notes 7.1

Algebra: 7.1 – 7.4 Monomials
Day
Section
Day 1
7.2
1. How do I multiply monomials?
Worksheet #1
Day 2
7.1
1. How do I simplify negative exponents?
Worksheet #2
Day 3
7.3
1. How do I simplify a monomial raised to a power?
Worksheet #3
Day 4
7.4#1
Day 5
Day 6
Essential Questions
1. How do I divide monomials?
Review of monomials
7.4#2
1. How do I divide monomials
Day 7
Review 7.1-7.4
Day 8
Review 7.1-7.4
Day 9
TEST 7.1-7.4
Assignment
Worksheet #4
Worksheet #5
Worksheet #6
Algebra: Chapter 7.1 – 7.4 Monomials
7.2 Notes: Multiplying Monomials
What is a monomial?
What is not a monomial?
When you multiply monomials, you _____________
the exponents!!!
Ex 1: Multiply.
a.
 y  y 
8
7

b. 2 y 4
 3 y 
c. (3x)( 2x 2 )
5
 2x
y 5 z   x 3 y 3 z 6 
e. (-5xy)( 4x 4 y 8 )
f.
h. (-5abc3)(4a3b6c)
i. (-5a)(6b)(7c)(-d)
2
d.
g.
 5 x  3x 
4
7
 b   c3  d 2   c  d 
j. (-6abc9)(4a2b7c)
***Fun Fact: if you multiply an odd number of negatives you will get a ____________________
If you multiply and even number of negatives you will get a __________________
7.1 Notes: Zero and Negative Exponents
Warm-Up: Complete the table. Use a calculator if necessary. Express all values as fractions (no decimals).
23 =
53 =
103 =
22 =
52 =
10 2 =
21 =
51 =
101 =
20 =
50 =
100 =
2 1 =
51 =
101 =
2 2 =
5 2 =
102 =
Can you make any conclusions about
negative exponents or zero as an
exponent?
Properties
Zero as an Exponent: For every nonzero number a,
Negative Exponent: For every nonzero number a and integer n,
Simplify each expression.
1. 37 0
2. 34
3.
5
5 2
5. 40
6.
1
50
7.
10s 2
12t
4.
3
6 1
8. 10x 3
9.
 3 
2
10. 4 h j
10 fg 5 h0
11.
h 2
 5stv 2 
12. 
3 
 6rm 
2. 2 4
3. 110
4.   5 
7. 4x 3 y 0
8.
2
4 3
You try it!
Simplify each expression.
1. 131
5.  15 p 
0
6.
2
51
8 m 2
4 n 1
2
0
7.3 Notes: Raising a monomial to a power
When you raise a monomial to a power you
_____________ the exponents!!!
Ex 1: Simplify.
3
a.  
  3  2 

b. 
2 3
3
Ex 2: Simplify.
a.
x 
d.
x y z 
g.
 2x y 
4 3
3
b.
5 8 3
3
 2a 
3
e.  3xy 
c.
 4x y 
f.
x 
c.
 2a b   ab 
2
2
5 9
4
.
5 3
Ex 2: Simplify:
 3s 
4 3
a.
3
s
2
1  2 3
xy
x y 
b.  2  
2 3 2
2 3
7.4#1 Notes: Dividing Monomials
Dividing Powers with the Same Base
We can use the properties of exponents to divide powers with the same base. Expand the numerators and
denominators. Then divide out each fraction…
35
=
33
46
=
47
When dividing two monomials with the same base you
__________the exponents!!
Ex 1: Simplify each expression.
33
a. 2
3
d.
x6 y9
x2 y5
y7
b. 4
y
m4
c.
m5
14 x3 y 9
5
e. 2 xy
18 y 8
2
3
f. 4 x ( y )
Ex 2: Simplify.
14 x9 y 9
12 10
a. 24 x y
48ab5c
13 9
b. 16b c
7.4#2 Notes: Dividing Monomials
Raising a Quotient to a Power
To raise a quotient to a power, raise the numerator and the denominator to the power and simplify if
possible.
5
n
  =
 p
2
3
  =
5
Ex 1: Simplify.
5 x 7 y
a. 10 x3 y 2
12m7 n1 p3
c.
6m1n2 p3
b.
m4 n2 p5
mn3 p5
 2x y 
1
4 xy
d.
Ex 2: Simplify.
 3x 4 
 3 
a.  2 y 
3
 3 x 4 y 


5 y 3 

b.
2
3
 5s 
 
6t
c.  
2
 31 abc 
 1 2 3 
e.  4 a b c 
 2 x 3 y 2 
 2 
d.  3 x y 
1
2