Lesson Page

 


  Math B

Laws of Rational Exponents

 

You have probably studied simplifying radicals, such as:
 

or

Radicals can also be expressed as a rational (or fractional) power of an expression.   It will sometimes be easier to use this new method of expressing a radical to simplify a radical expression.  

When you see a radical expression,
you can convert it to a fractional power.

Specifically,  

 or in General:        


Notice:   The index of the radical becomes the denominator of the
rational power, and the exponent of the radicand (expression inside
the radical) becomes the numerator.

Look at these examples:

(1)   

(2)   

(3)   

 


Remember the Rules of Exponents?
They are still valid for rational exponents!!!

Rule Example

 

Simplifying radicals is often easier using rational exponents.

Look at this "rational" example,
solved two ways.     ==>
 

Simplify:  

Solved by Rationalizing the Denominator

Solved by Using Rational Exponents


Check out how these problems are done using the rules of exponents:

Evaluate: 

Evaluate:  

 


           F. Roberts