Math 2
Lesson 1-3: Exponent Rules: Power to a Power Rule
Name____________________________
Date __________________________
Learning Goal:

I can use exponent rules to simplify expressions involving a power to a power, including integer and
variable bases.
Part I: Power to Power Rule
Quick Poll: How do you write the expression (34 )5 as a single base with an exponent? ___________
i.
To check your response we will expand the factors and simplify.
(34 )5  34 34 34 34 34 
Were you correct?
ii.
Now expand the factors and simplify, (m4 )5 
iii.
Now expand the factors and simplify, ( x 5 )3 
1. Generalize the pattern you found above:
x 
a b
 x _________
2. Use your new rule to write the following expressions as a single base with an exponent.
a.)
7 

b.)
b 

c.)
100 
d.)
t 
e.)
12 
f.)
b 

g.)
t 

h.)
7 

3 2
2 4
3 4
5 3

3 6
8 4
5 7
3 r


OVER 
Page 2
Quick Poll: How do you simplify the expression (2 x 4 )3 ? ___________
i.
To check your response we will expand the factors and simplify.
(2 x 4 )3  2 x 4 2 x 4 2 x 4 
Were you correct?
ii.
Now expand the factors and simplify,  2xy  
iii.
Now expand the factors and simplify,  3m 2 n 4  
4
4
1. Generalize the pattern you found above:
2. Use exponent rules to simplify as much as possible.
a.)
(3m4 n7 )5 
b.)
( 3x 3 y )4 
c.)
 4x
d.)
 3x
e.)
2 x 2 y  4 x 4 y 3 z  yz 3 
f.)
x 3 y  3x 2 y 2 
4
2
y3z  
2
y8 z6  
3
2
9z4 z3
3

k
x y   (k )
a
x ____ y ____
Page 3
Part II: Fraction Power to Power Rule
3
 x4 
Quick Poll: How do you simplify the expression  2  ? _________
y 
i.
To check your response we will expand the factors and simplify.
3
 x4 
x4 x4 x4
x4 x4 x4



 2
y2 y2 y2
y2 y2 y2
y 
Were you correct?
5
ii.
4
Now expand the factors and simplify,   
n
iii.
2
Now expand the factors and simplify,  c  
3
n
x
a __
a
   __
b
b
1. Generalize the pattern you found above:
2. Use exponent rules to simplify as much as possible.
4
d.)
f.)
a 2  2ab3 
3
2
7
a.)   
8
b.)
 2x 
 3 
z 
2
8ab 2
c.)
 3a bc 
2

e.)
 3a 6 


2 
 2b 
3 2
27 a 3b 4 c 6

(23 xy 2 )2

22 xy 3
OVER 
Page 4
Homework:
Simplify each expression.
1.
x 
5.
 23 
2 3

4 5

9.  8c5  
y
 c h 
15.
3y   x y z  
18.
6 2
a 
6.
 2 y 
7 5

5 4

10.
12.
5 6 4
2.
y 

4.  52  
7.
4y 

8.
10 4
3 2
 3h 
9 3

3
2
16.
 4h   2g h 
3 2
3
6
 5c 
19.  2  
c 
4
 4s 6 
22.  3 5  
 tr 
x
  
 y
 3w 
21.  6  
g 
3
 2d 4 
24. 
 
 4e 
3
13.   h9 k 7  

5
3.
3
11.
y d 
14.
k  k 
4
6 8
9 5


3 2

2
3
 5c 
20.  2  
 d 
2
3
3
3 2
17. 14a 4b6   a 4c3  

2
 72 
25.  3  
3 
4  y 
2
 2d 11 f 6 
23. 
 
f8 

2
 65 
26.  4  
6 
27.
x 2 y 3  2 xy 4 
 3x y 
4
2 2
3
