SOLUTION: how an expression with a rational exponent can be rewritten as a radical expression?

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Question 455917: how an expression with a rational exponent can be rewritten as a radical expression?
Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!





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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The laws for rational exponents work exactly the same as the laws for integer exponents. Here is a review of the laws of exponents


Exponent Laws:

Product Law: x%5Ea%2Ax%5Eb=x%5E%28a%2Bb%29

Power to a Power: %28x%5Ea%29%5Eb=x%5E%28a%2Ab%29

Product to a Power: %28xy%29%5Ea=x%5Ea%2Ay%5Ea%29

Quotient Law:x%5Ea%2Fx%5Eb=%28x%29%5E%28a-b%29%29
Quotient to a Power :%28x%2Fy%29%5Ea=x%5Ea%2Fy%5Ea%29%29
Let's look at this problem:

25%5E%281%2F2%29
To convert a rational exponent to a radical the denominator becomes the index and the numerator of the exponent stays with the number or variable and is in the radicand


So 25%5E%281%2F2%29=+sqrt%2825%29