Fractional exponents

Fractional exponents are another way to write powers and roots. When a power is a fraction, the numerator indicates the power the base is raised to, and the denominator indicates the root the base is raised to.


The order that you take the root or power does not matter - the answer will always be the same in the end. Sometimes, it is more convenient to compute the root portion of the fractional exponent first. For example, when calculating to the power of , since the cube root of is , it is easier to compute the result by determining the cube root first:


When the denominator of the fractional exponent is , you are taking the square root of the base to the power of the numerator. If the fraction can be simplified, simplify it.


When using a calculator, you can take the base to the power of a decimal, but if you are not using a calculator, leave it in fractional format when trying to compute the exponent.