Question 679089: How can I explain an irrational exponent?
Found 2 solutions by lynnlo, MathLover1:
Answer by lynnlo(4176)   (Show Source):
You can put this solution on YOUR website! A IRRATIONAL CAN NOT BE WRITTEN AS A FRACTION
EXAMPLES:
PI
(SQUARE(2)
IF YOU CAN RAISE A NUMBER TO ANY OF THESE
YOU WOULD HAVE A IRRATIONAL EXPONENT
Answer by MathLover1(20850)  (Show Source):
You can put this solution on YOUR website! recall that, by definition, an exponent can be any number, real or complex, negative or positive, rational or  , algebraic or transcendental.
 is an example of an irrational exponent
or  ....how to do this one?
we will do it by  the exponent by  exponents that are closer and closer to the irrational one
In example , you want the exponent  to be  equal to  , so the first approximation to is  .
or, go one step further with  , so the second approximation to is  which is approximately 
or three significant figures,
 , so you have to take a  which is approximately  Continuing this way, we get the sequence of approximations:
 , ,  ,  ,  ,  ,  , ...
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