Power of a Product Property of Exponents
Property â€”
Power of a Product Property of Exponents
English To raise a product to a power, you can first raise each
factor to the power. Then multiply.
Algebra (xy)^{n} = x^{n}y^{n} (Here, n is a positive integer.)
Example (2x)^{3} = 2^{3}x^{3} = 8x^{3}
Example 1
a. Use the Power of a Product Property of Exponents to simplify (3y)^{2}.
b. Use the definition of exponential notation to justify your answer.
Solution
a. Raise each factor to the power 2. 
(3y)^{2} 
= 3^{2}y^{2} = 9y^{2} 
b. Rewrite the power to show
the factors. Then simplify. 
(3y)^{2} 
= (3y) Â· (3y)
= 3 Â· 3 Â·
y Â· y
= 3^{2}y^{2}
= 9y^{2} 
Example 2
Simplify: (2^{3} Â· w^{5})^{4}
Solution
Use the Power of a Product Property
of Exponents to raise each factor inside
the parentheses to the power 4. 
(2^{3}
Â· w^{5})^{4} 
= (2^{3})^{4}(w^{5})^{4} 
Use the Power of a Power Property
of Exponents. Simplify. 

= (2^{3 Â· 4})(w^{5}^{
Â· 4}) = 2^{12}w^{20} 
Note:
We left 2^{12} in exponential form. To
evaluate 2^{12}, use the â€œy^{x}â€ key on a
scientific calculator or the â€œ^â€ key
on a graphing calculator.
2^{12} = 4096
