Math 2 Honors
Lesson 1-2: Exponent Rules - Product and Quotient
Name________________________________
Date ____________________________
Learning Goal:

I can use exponent rules to simplify expressions involving products and quotients, including integer
and variable bases.
An exponent tells you how many times the base is multiplied by itself.
Part I: The Product Rule
Quick Poll: How do you write the expression 23 24 as a single base with an exponent? ___________
i.
To check your response we will expand the factors and simplify.
23 24   2 2 2  2 2 2 2  
Were you correct?
ii.
Now expand the factors and simplify, 34 37 
iii.
Now expand the factors and simplify, x5 x 2 
Generalize the pattern you found above:
x a  xb  x ___________
Product Rule
1. Products of Powers: In parts a – f, write the expression as a single base with an exponent, if possible.
a.)
4  4  
b.)
 x  x  
c.)
 2  2  
d.)
b 4  b5 
e.)
45  32 
f.)
a5  b2 
5
2
3
4
5
6
2. How is 1e and 1f different from 1a – 1d? ____________________________________________
OVER 
Page 2
3. Use the Product Rule to simplify the expressions, if possible.
a.)
32  36 
b.)
y8  y 
c.)
t3  t5  t2 
d.)
a 3 b5 
e.)
a 9 b2 a 2 
f.)
r r
g.)
( 2)3 ( 2)7 
h.)
q 3 q5 
i.)
z 3 z 5 
j.)
t 3  t 7  t 
k.)
a 9 b 2 a 2 b3 
l.)
115 c 2 116 c 1 
m.)
x4 y 3 z5 x2 y8 z 
n.)
32 rs3t 5 3r 2 s5t10 
Quick Poll: How do you simplify the expression 2 x 3 3x 4 ? ___________
i.
To check your response we will expand the factors, use the commutative property to rearrange the
factors and simplify.
2 x3 3x 4   2 x x x  3 x x x x   2 3 x x x x x x x 
Were you correct?
ii.
Now expand the factors and simplify, 3t 4 9t 3 
iii.
Now expand the factors and simplify, 3x 5 2 x 
4. Use the Product Rule to simplify the expressions, if possible.
a.)
3x 2  2 x 5 
b.)
5y4  3y 
c.)
2t 4  3t 5  7t 3 
d.)
7a 3 4b5 
e.)
5a 5 2b3 7c 2 
f.)
9r 2r 
g.)
( 2)3 x ( 2)7 x 4 
h.)
6q2 3q4 
i.)
3z 1 5z 3 
j.)
3t 2  4t 7  3t 
k.)
4a 3b2  6a 7 b2 
l.)
22 c3 32 c 2 
Page 3
Part II: The Quotient Rule
55
as a single base with an exponent? ___________
53
To check your response we will expand the factors and simplify.
Quick Poll: How do you write the expression,
i.
55 5 5 5 5 5

 1 1 1 5 5  25
53
5 5 5
Were you correct?
ii.
Now expand the factors and simplify,
t6

t2
iii.
Now expand the factors and simplify,
t2

t6
bx
 b __________
y
b
Generalize the pattern you found above:
Quotient Rule
1. Quotients of Powers: In parts a – g, write the expression as a single base with an exponent, if possible.
a.)
25

23
c.)
158

158
e.)
x5

x14
b.)
89

85
d.)
b7

b2
f.)
x6

y5
2. Use the Quotient Rule to simplify the expressions, if possible.
a.)
32

36
b.)
y8

y
c.)
t3

t
d.)
a3

b5
e.)
a 9 b2

a4
f.)
2r

6r
g.)
( 2)3

( 2)7
h.)
48q3 z 7

4q 7 z 3
i.)
28r 45 z 5

7z3
j.)
22 x5 y 2

36 x 3 y 5
OVER 
Page 4
Part III: Homework
Directions: Use the rules from the investigation to simplify the following expressions. You should NOT
NEED A CALCULATOR for these problems. Show all work.
1.
88   885    882    886  
2.
x x 
3.
x5  x 2  x 6 
4.
5a9 2b10 3c 2 
5.
x5  x12  y 4  y 
6.
x5  x 2  x 6 
7.
9r (10r ) 
8.
9r  10r 
9.
a 1 5a3 a 1 8a3 
10.
(5wx 7 y 5 )(7 w3 x10 y 12 )  11.
8 x5  x 2  3x 7 
12.
y y y 
13.
8819

8814
14.
x19

x14
15.
p4

p6
16.
x

x
17.
19.
x  2y

x  2y
20.
3x15 y 2

y8
(12)3

(12)7
18.
21.
3x 2 y 2

12 x5 y 4
t

t8
Solve the following equations. Show all work.
22.
2x + 8 = -5x – 10
23.
2x + 8 = -5(x – 10)