Dividing with Exponents
Algebra I
Chapter 8.2
Name: ____________________________________
Date: _________________________ Hour: _______
Exponent Properties: The Quotient Rule
Quotient
Repeated multiplication
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Power of the
form 𝑎𝑏
23
22
2∙2∙2
2∙2
2∙2∙2
2∙2
21
37
34
𝑥 10
𝑥4
512 𝑦 20
57 𝑦 8
Too big to write out! Find another way.
𝑎7 𝑏 3
Now, determine a general rule for what happens when we have two exponential
expressions dividing each other with the same base. You may want to write the rule in
words, or you can use an example or expression to communicate the rule.
Please write the algebraic rule we came up with as a class:
Try some examples:
(a)
y5
y3
(b)
810
84
(c)
54  58
57
(d)
(3)9
(3)
(e)
2m8
m6
(f)
45 
1
42
Exponent Properties: The Distributive Rule for Quotients
Quotient
Repeated multiplication
Write as a fraction
2 4
( )
3
2 2 2 2
( )( )( )( )
3 3 3 3
24
34
3 3 3 3 3 3
( )( )( )( )( )( )
5 5 5 5 5 5
86
26
2𝑥 3
( )
9
310 × 𝑎10
1210 𝑏10
𝑎 𝑛
( )
𝑏
Too hard to write out! Find another way.
Now, determine a general rule for what happens when we have a quotient raised to a
power. You may want to write the rule in words, or you can use an example or
expression to communicate the rule.
Why is this rule called “the distributive rule for quotients?”
Please write the algebraic rule we came up with as a class:
Try some examples:
(a)
(d)
 6
 
 r
3
(b)
x
 
 y
(e)
 6
 
 r
13
a
 
b
3
9
(c)
1
 
 y
(f)
 m4  m 

2 
 5m 
44
3