Download Math 1 - Mayfield City Schools

Math 2
Lesson 1-2: Exponent Rules - Product and Quotient
Name________________________________
Date ____________________________
Learning Goal:

I can solve problems using properties of exponents learned in previous courses, extending the
properties from integer bases to 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 c2 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, 3x5 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.
b.)
y8

y
c.)
t3

t
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
a.)
32

36
d.)
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)