8.3 Division Properties of Exponents
When we multiplied powers with same bases, we added the exponents.
m n
a
∙ a = a m+n
Make a conjecture (educated guess) about the rule for dividing powers.
4
7
___
4
4 Quotient of Powers Property a
m
__ = a
a
m ­ n
n
6 3 ∙ 6 5
9
6
1/y 5 ∙ y 3
2/x 4 ∙ x 2 1
Power of a Product (ab)
m
= a
m m
b
(4x 2 y 3 ) 5
Power of a Quotient Property
(2/3) 3 4
(­3/y)
­3
(x/y)
Summary of all Rules
a m∙a n = a
m+n
(a m) n = a
mn
(ab)
m
m m
= a
b
a 0 = 1
a ­n = 1/a
n
a m/a n = a
(a/b)
m
= a
m­n
m m
/b
2
Let's put all the rules to work now!
2x 2 y ∙ 9xy 2
3x y 4
(2x/y 2 ) 4
(3x 2 z 4 /2xz)
­3
(a 3 ) 5 /(a 4 ) 5
18b 2 c ∙ (3ab) ­ 2
2 3
4bc 5a
c
(3/4) ­1 ∙ (2a 3 x 5 ) 2
­3 ­1 ­3
(a
x )
3