Sect 5.1 - Exponents: Multiplying And Dividing Common Bases Worksheet With Answers Page 4
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Division of Like Bases (The Quotient Rule for Exponents)
If m and n are positive integers where m ≥ n and a ≠ 0, then
m
a
m – n
= a
. In words, when dividing powers of the same base, take
n
a
the exponent in the numerator minus the exponent in the denominator and
keep the same base.
Simplify the following:
24
93
x
8
Ex. 8a
Ex. 8b
6
31
x
8
8
6
3
y
x
y
Ex. 8c
Ex. 8d
2
y
xy
Solution:
24
x
24 – 6
18
a)
= x
= x
.
6
x
93
8
93 – 31
62
b)
= 8
= 8
31
8
8
y
8 – 1
7
c)
= y
= y
y
6
3
x
y
6 – 1
3 – 2
5
1
5
d)
= x
y
= x
y
= x
y.
2
xy
Concept #4
Simplify Expressions with Exponents
Simplify:
6
7
5
− 28x
y
z
3
4
7
3
Ex. 9a
(– 4a
b
c)(7a
bc
)
Ex. 8b
2
4
21x
yz
2
5
4
2
(−6a
b
c)(−5ab
c
)
Ex. 9c
2
(−10ab)(ab
)
Solution:
3
4
7
3
a)
(– 4a
b
c)(7a
bc
)
(use the commutative and associative
properties of multiplication to group common bases together)
= – 4 • 7a
3
• a
7
• b
4
• b • c • c
3
3 + 7
4 + 1
1 + 3
= – 28a
b
c
10
5
4
= – 28a
b
c
.
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