Rational Exponents and Radicals

By: Ethan Darley

What are Rational Exponents and Radicals

Rational Exponents are just as they say, but they also have a fraction as an exponent. There job is to be converted from rational exponential form into a radical to simplify a problem.


Radicals are any root (square, cube ,quad) simplified from a Rational Exponent. The job of a Radical is to either be changed into a Rational exponent or to stay the same.

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How to convert Rational Exponents and Radicals

To convert Rational exponents into radical form you first need to put the exponent into a root, this is dependent based on what number the denominator is for the exponent. Next you keep the rational number leftover numerator is now the exponent for the rational number. Then you put the rational number and its exponent into the square root. Then you see how many times the exponent of the rational number can go into the number of the root it is in. lastly based on the amount of times the exponent goes into the root is how many of the exponents should be on the outside of the square root, then its remainder stays with the rational number.


To convert Radicals into Rational Exponent you first take then number in the root that it is in and move it out of it. Next for the fraction (exponent) the numerator is the number that is to the far right of the root that it is in. The denominator is the number that defines what type of root the number was originally.

Any Questions

If you are still confused or are looking for more answers to questions with greater complexity click the video on the bottom of the page for a better understanding or subscribe to "wallaceopenmath" for more of his videos.
Convert Rational Exponents and Radical Expressions