Transcript Notes 2 - Henrico

Monomials
Dividing and Reducing Monomials
The Zero Power Rule
Zero Property of Exponents
A nonzero number to the zero power is 1:
a  1, a  0
0
1) 7  1
0
2) 4a  1
0
3) 2a b w   1
7 4
0
Quotient of Powers
7
Simplify the following expression:
a
5
a
•Step 1: Write out the expressions in expanded form.
a
a  a  a a  a  a  a
5 
a
a  a a  a  a
7
•Step 2: Cancel matching factors (A factor is a term that is
multiplied by the rest of the expression; here, ‘a’ is a factor.).
a
a  a  a a  a  a  a a 2
2

a
5 
a
a  a a  a  a
1
7
Quotient of Powers Rule
Let’s look at the results:
a7 a2
2
a
5 
a
1
Notice:
• the base is still ‘a’.
• the power is 2 = (7 - 5).
• the term that didn’t cancel is in
the numerator (where the larger
power was to begin with).
For all values, a, and all integers m
and n:
am
m n
 a , a  0.
n
a
Quotient of Powers Rule
1)
2)
3)
4)
a5
7 
a
5
w
2 
w
5
6
7 
6
52
2 
5
1
2
a
3
w
3
w
1
1
1
2 
6
36
5 1
0
Dividing Monomials
These monomials have coefficients and more than
one variable. Reduce the coefficients as you
would with a typical fraction and use the power
rule for the variables.
x 3y 8
x5 y9
3 8
xy
1) 2 
1
xy
3
15x 4
2)
2
6 
5x
25x
36a 5 b3 9a 3
3)
6
2 9 
5b
20a b
Power of a Quotient
3
3
Simplify the following:  
2 
Step 1: Distribute the power to both the numerator
& denominator.
3
3
3
3
  
2  23
Step 2: Find the powers of the numerator & denominator.
3
3   27
2 
8
Step 3: Reduce if you can.
Power of a Quotient Rule
m
 a
am
For any numbers, a & b, and all integers m,
 b   bm .
10
a
a 
1)  2   20
b 
b
3
3
1
1
1 

2)    3 
5 125
5
2
3x 2
9x 2
 3x 

3)  2  
2
4
2
7y 
7y  49y
3
30