This document discusses dividing exponential forms, monomials, and polynomials. It contains the following key points: 1. Exponential forms with the same base can be divided using the quotient rule for exponents. 2. Monomials are divided by dividing the coefficients and using the quotient rule for exponents of like bases. 3. To divide a polynomial by a monomial, each term in the polynomial is divided by the monomial.

1. Exponent Rules and Dividing
Polynomials
5.6
1. Divide exponential forms with the same base.
2. Divide monomials.
3. Divide a polynomial by a monomial..

2. Objective 1
Divide exponential forms with the
same base.

3. Quotient Rule for Exponents
If m and n are integers and a is a real number,
where a 0, then
 .
m
m n
n
a
a
a


3
7
2
2
2
2
2
2
2
2
2
2
2
2
2
2
3
7









4
4
3
7
2
1
2
2
2
2
2
2
2
2
2
2
2
2
2











1 1 1
1 1 1

4. When an equation in one variable is solved the answer is a point on a line.
Divide:
14
6
j
j
3
5
u
u
3
6
m
m
2
2
3
5
y
x
y
x
2
u 8
1
j

8
14
6 

 j
j
9
3
6 


 m
m 9
1
m
 y
x3

5. Objective 3
Divide monomials.
2

6. Copyright © 2011 Pearson Education, Inc.
Divide.
3 6 2
4 3
18
24
x y z
x y
3 6 2
4 3
18
24 1

x y z
x y
3 4 6 3 2
18
24
 
 x y z
1 3 2
3
4

 x y z
3 2
3 1
4 1 1

y z
x
3 2
3
4

y z
x
  
  
  

7. 1
24
18 2
3
6
4
3
z
y
y
x
x




Divide.
3 6 2
4 3
18
24
x y z
x y
3
1
24
18 2
3
6
4
3
z
y
y
x
x




4
1
x
y3
1
x
z
y
4
3 2
3


8. Dividing Monomials
1. Divide the coefficients or simplify them to
fractions in lowest terms.
2. Use the quotient rule for the exponents with like
bases.
3. Write the final expression so that all exponents
are positive.

9. When an equation in one variable is solved the answer is a point on a line.
Divide:
7
2
4
5
42
28
q
p
r
q
p
3
2
4
5
4
4
y
xy
xy
xy 64
43

3
3
3
2
q
r
p

10. Objective 4
Divide a polynomial by a monomial.
3

11. 5
2
7
4
5
2
5
7
5
4 




5
2
5
7
5
4
5
2
7
4





From arithmetic…
or

12. Divide.
6 2 3
2
36 9 6
3
 
x y x y x
x y
6 2 3
2 2 2
36 9 6
3 3 3
  
x y x y x
x y x y x y
4 2
12 3
x y x
xy
  
Divide each term in the
polynomial by the monomial.

13. If a, b, and c are real numbers, variables, or
expressions with c 0, then
Dividing a Polynomial by a Monomial
Divide each term in the polynomial by the
monomial.
 .

 
a b a b
c c c