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Power of a Product and Power of a Quotient
Let a and b represent real numbers and m
represent a positive integer.
Power of a Product Property
a b
m
 a b
m
m
Power of a Quotient Property
m
a
a
   m, b0
b
b
m
• Example 1
 3x 
4
Apply the power of a product property:
4
4
4
3x
   3  x  81x
4
• Example 2
 4x y 
2
3
2
Apply the power of a product property:
 4x y    4   x    y 
 16   x    y 
2
3
2
2
2
2
2
2
3
3
2
2
Now apply the power rule for exponents:
 16x y
4
6
• Example 3
3
 
x
3
Apply the power of a quotient property:
3
27
3
3
   3  x3
x
x
3
• Example 4
 2x 
 3 
 y 
2
4
Apply the power of a quotient property:

2x
 2x 
 3 
3
y
y


2
4
2
 

4
4
2x 


y 
2
3
4
4
Now apply the power of a product property in
the numerator:

 
y 
 2 
4
 x
3
4
2
4

 
y 
16  x
3
2
4
4

 
y 
16  x
3
2
4
4
Now apply the power rule for exponents:
8
16x
 12
y