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

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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) About Me  (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) About Me  (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 p%2Fq, where q+%3C%3E0, then the number is said to have rational+exponent.
For example: 8%5E%281%2F3%29, means to take the 3-th root of 8

Exponents can accept values from the multitude of the real numbers. They can be both rational or irational.
Irrational exponents:
Let x be an irrational number. Then, for a rational number m%2Fn arbitrarily close
to x we can find a unique value +b+%3E+0 so that the rational exponent +a%5E%28m%2Fn%29 becomes arbitrarily close to b. We call such value b the irrational exponent a%5Ex.