When dealing with fractional exponents, remember this form:

  is the index of the radical which is also the denominator of the fraction,  represents the base of the exponent, and  is the power the base is raised to. That value is the numerator of the fraction.

With a negative exponent, we need to remember this form:

  represents the base of the exponent, and  is the power in a positive value.

 To get rid of the radical, just multiply top and bottom by the radical. 

A fractional exponent means to take the number to the power of the numerator and to the root of the number in the denominator.

Take 81 to the power of 3 and to the root of 2 (square root). These can be done in either order but it is usually easier to take the root first.

Alternatively, this is what it would look like cubing 81 first.

First, distribute the exponent to both the numerator and denominator of the fraction.

The numerator of a fractional exponent is the power you take the number to and the denominator is the root that you take the number to.

You can take the cubed root and square the numbers in either order but if you can do the root first that is often easier.

This is the answer. Alternatively, you could have squared the numbers first before taking the cubed root.

When an exponent is a fraction, we convert to radical form. 

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

When an exponent is a fraction, we convert to radical form. 

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

Although we see a negative number there, keep in mind the fractional exponent.

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

We know it's a cubic root and any number cubed can generate negative answers.

In general, any odd exponent can generate negative answers. 

When an exponent is a fraction, we convert to radical form. 

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

To eliminate the radical in the denominator, remember to multiply top and bottom by itself. 

When an exponent is a fraction, we convert to radical form. 

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

When an exponent is negative, we rewrite in this form in terms of fraction:

 is the base while  is the exponent and it's going to be a postive number when written in a fraction.

 is the exponent from the numerator of the fraction,  is the index from the denominator of the fraction and  is the base of the exponent.

When we have fractional exponents, we convert like this:

.  is the index of the radical which is the denominator of the fractional exponent,  is the power that will raise the base which is the numerator of the fractional exponent and  is the base.