How to Factor Fractional Exponents

A fractional exponent is an exponent where the numerator of the fractional exponent acts as a typical exponent while the denominator is the index of a root. For example, x^(1/2) is equivalent to the square root of x and x^(3/2) is equivalent to the square root of x^3. Understanding how to factor fractional exponents is necessary for high school algebra, calculus and higher-level mathematics courses.

Things You'll Need

• Pencil
• Paper

Instructions

1. Factor the expression until all you have remaining that needs factoring are the fractional exponent parts of the expression.

2. Identify potential ways to factor the expression. For example, if the expression is (x-2)^(5/2) + (x+2)(x-2)^(3/2), then (x-2)^(1/2) could be factored out, or (x-2)^(3/2) could be factored out.

3. Identify the greatest common factor. In the above example, (x - 2)^(3/2) is the greatest common factor.

4. Factor out the greatest common factor. In the example in Step 2, the result after factoring out the greatest common factor is (x-2)^(3/2) * [(x-2) + (x+2)] = (2x)(x-2)^(3/2).

Tips & Warnings

• Remember that exponents basically represent repeated multiplication. In the case of fractional exponents, x^(3/2) is equal to x^(1/2) * x^(1/2) * x^(1/2), since you add the exponents when you multiply exponents with a common base. Remember this rule when factoring fractional exponents.

References

• Math Warehouse: Simplify Fraction Exponents