Fractional Exponents

The last area of power functions to be addressed is the case of a fractional exponent. In order to express a radical expression without a radical sign, fractional (or rational) exponents are used. Some radical expressions and their equivalent rational exponent expressions are below:

Fractional exponents are much easier to manipulate in solving equations than radicals, because all of the exponent rules apply to rational exponents. In general, roots can be written with fractional exponents in the following manner:

Roots as Fractional Exponents:

The value on the radical becomes the denominator of the fractional exponent. The exponent on the value beneath the radical becomes the numerator of the fractional exponent.

Example 1 Simplify

Apply the Product of a Power Rule.

Example 2 Simplify .

Apply the Power of a Power Rule.

Example 3 Simplify .

Apply the Quotient of a Power Rule

Example 4 Simplify .

Apply the Power of a Quotient Rule.

To learn how to simplify expressions involving fractional exponents, select the following links:

Fractional Exponents #1

Fractional Exponents #2

To solidify your understanding of rational exponents, visit the following link to Holt, Rinehart and Winston Homework Help Online. It provides examples, video tutorials and interactive practice with answers available. The Practice and Problem Solving section has two parts. The first part offers practice with a complete video explanation for the type of problem with just a click of the video icon. The second part offers practice with the solution for each problem only a click of the light bulb away.

Guided Practice

Fractional Exponents Worksheet

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Fractional Exponents Answer Key

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