Rational Exponents
Before we rewrite an exponential expression as a radical, we must make
sure that the rational exponent is reduced to lowest terms.
Example 1
Simplify and write using only positive exponents: w^{1/3}
Â· w(^{3/2}) = w^{1/6}
Solution
Each factor has the same base, w.
Therefore, add the exponents and keep w
as the base.
Write each fraction with the LCD, 6.
Add the exponents.
Simplify. 
w^{1/3}
Â· w(^{3/2}) = w^{1/6}
= w^{1/3 + (3/2) + 1/6
}
= w^{2/6  9/6 + 1/6}
= w^{ 6/6
}
= w^{ 1} 
Use
to write the expression using
a positive exponent. 

Therefore,
Example 2
Simplify and write using only positive exponents:
Solution
There is more than one way to start simplifying.
We begin with the Power of a Quotient Property. 

Use the Power of a Product Property to raise
each factor to the power 3. 

Use the Power of a Power Property. 

Use the following to write the coefficients with
positive exponents:


Evaluate the coefficients and simplify


So,
Note:
We could use radical notation to write
