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1) Be able to apply the quotient of powers property.
2) Be able to apply the power of a quotient property.
3) Be able to apply the multiplication properties of exponents.
P ro d u c t o f P o w ers P ro p erty : a a am n m n
P o w er o f a P o w er P ro p erty : a am n m n
P o w er o f a P ro d u c t P ro p erty : a b m m ma b
Z ero E x p o n en ts: a a0 1 0 ,
N eg ativ e E x p o n en ts : aa
ann
1
0,
Evaluate the following expression:
3
3
5
3
Solution
3
3
3 3 3 3 3 3
3 3 33 3 3
3 3 3
3 3
1
1 3
3
5
3
2
2
Please note the following things:
1. The base is still the same: 3.
2. The exponent now has a value of 2 and (5-3)=2.
To divide powers that have the same base, subtract the exponents.
a
aa a
m
nm n , 0
Simplify the quotient.
A . x
x B .
C . (-2 )
(-2 ) D .
7
3
4
6
6
4
6
7
7
y
y
A .
x
xx
x
7
37 3
4
Solutions
B . 6
6
4
6
6
6
1
61
36
4 6
2
2
C .
2
22
2
8
44 1
3
D . y
yy
y
,
y
7
77 7
0
1
0
Simplify the following quotient:
3
2
3
1) Find the power of the numerator.
2) Find the power of the denominator.
3) Divide.
3
2
3
227
8
3 3
3
Power of a Quotient Property
a
b
a
bb
m m
m
, 0
Use the power of a quotient property to simplify the expressions.
A . 3
4 B .
C . D .
3 4
5 3
2
3
2
x
y
rSolutions
A .
3
4
3
427
64
3 3
3
B .
2 2
16
4 4
4
4
x x
x
C .
y y
y
3 3
27
3 3
3
3
D .
2
2
8
3 3
3
r
r
r
1. Simplify the following quotients.
A . 2
2 B .
-5 C . D .
a
c E .
2
-3
5 4
5 7
9
9
3 2 4 3
9
y y
2. Simplify the following expression.
7 33 4
2 2
1x y
x y
xy
xy
A .
=
2
22
2
64
2
42 4
6
( )
B . -5
-5
9
99 9
0
5
5
1
C .
4
5
4
564
125
3 3
3
D . a
c
2 2
2
2
c
a
c
a
E .
y y
y
y
y
y
y
y
4 3
9
4 3
9
7 9
2
2
1
Step 1. Gather like terms.
7 3 13 1
2
4 1
2
x x
x x
y y
y y
Step 2. Rewrite using positive exponents.
7
3
12 3
4 2
x x x x
y y
y yStep 3. Apply the product of powers property
7
3
17
6
2 x
y
yStep 4. Apply the quotient of powers property.
7
3
17
4 x
y
Step 5. Write the final answer.
7
3
4
7
y
x
