SOLUTION: How would you define what a rational exponent is? Is there such a thing as an irrational exponent? Explain.

Question 672074: How would you define what a rational exponent is? Is there such a thing as an irrational exponent? Explain.

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
How would you define what a rational exponent is? Is there such a thing as an irrational exponent? Explain.
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Rational : any number which can be expressed in the form a/b where
a and b are integers and b is not zero.
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Yes there are irrational exponents:
Example:
2^(sqrt(3)) = 3.32199.......
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Cheers,
Stan H.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
Definition:
If the power or the exponent raised on a number is in the form , where , then the number is said to have .
For example: , means to take the 3-th root of

Exponents can accept values from the multitude of the real numbers. They can be both rational or irational.
Irrational exponents:
Let be an irrational number. Then, for a rational number arbitrarily close
to we can find a unique value so that the rational exponent becomes arbitrarily close to . We call such value the irrational exponent .

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