4.2 Warmup
Name______________________
1. Use the exponent laws to rewrite each expression as a single power.
a) (x3) (x5)
2.
b  b 
5
y8
y2
c)
b2
Use the exponent laws to rewrite each expression as a single power.
b)
5 2
a) (x )
3.
b)
y7
 
y2
3
3
c) (b2) (b4)
Simplify each expression.
a) (2x3)
2
b) (4y2)
3
c) (3x6y5)
2
4
4.
Write an explanation for each of the exponent laws.
Exponent Law
Product of Powers
(a m )(a n )  a m  n
Quotient of Powers
am
= am – n, a  0
an
Power of a Power
n
(a m ) = a mn
Power of a Product
(ab)m = (am)(bm)
Power of a Quotient
n
an
a
   n
b
b
,b0
Zero Exponent
a0 = 1, a  0
Explanation and Example
When multiplying powers of the same
base, add the exponents
28 25   213
FCP 10
Date:________________
4.2a Integral Exponents
Look for patterns and then complete the following tables. What is happening to
the value in each table? What is happening to the exponent? Leave answers as
fractions rather than decimals.
Power
Value
Power
Value
Power
Value
24
16
34
81
104
10 000
23
8
33
27
103
1000
22
32
9
102
100
21
31
101
20
30
100
31
101
21
1
2
22
32
What patterns do you observe?
What does a negative exponent appear to do?
Rewrite the following with positive exponents:
1
9
102
1
10
1

7 1
Thus we have the following exponent properties:
34 
1

28
52 
a n 
1
a
n
ie: 57 
2
Note also that  
5
1
, a 0
3

a
1
57
n
 an , a  0
1
 26
26
ie:
3
1
3
2
 
5
2
 1 
5
3
5
 1  
2
3
5
  
2
a 
 
b 
Or, to change the sign of an exponent, reciprocate the base.
1. Rewrite each of the following using only positive exponents
a) 83
d)
1
5 7
b) a 2b 3c 1
9
e)  
 13 
2
c) 2x 3y 4
f)
x 3
y 4
n
n
b 
 
a 
2. Using exponent laws, rewrite the following with a single, positive exponent:
b)
 0.7  0.7 
c)
d)
x 6
x 2
e)
3y 
4
3y 
52 53
f)
54
g)
7 
h)  x 3  x 6 
j)
 a 5 
 2 
a 
a)
3 3 
9
5
2
3
5
2 3
2
2
 4 3  4  2 
K)     
 5   5  
4
a8
a 4
i)
a  a  a 
l)
 5w 
2
6
 5w   5w 
1 2
3 2
3
3. Simplify each expression, and restate using only positive exponents:
a)
5  26 
2 5 
8
3
d) 5xy 3  2x 4y 
g)
5mn 
2 3
 5x 
j) 
1 
 2y 
2
b)  7  32 
e)
 84 
c)  5 
3 
 2m n   5m n 
3
1
h) –3a (2a)
K)
3
-4
1.3  10 4
2.5  10 6
4
2
f)
2
w 4 y 3
wy 3 w 6y 2 
 8xy 6 
i) 

2
 16x y 
1