Factoring Expressions with Fractional or Negative Exponents Expressions with fractional or negative exponents can be factored by pulling out a GCF. Look for the variable or exponent that is common to each term of the expression and pull out that variable or exponent raised to the lowest power. These expressions follow the same factoring rules as those with integer exponents. For instance, 2x14+5x342{x}^{\frac{1}{4}}+5{x}^{\frac{3}{4}}2x41+5x43 can be factored by pulling out x14{x}^{\frac{1}{4}}x41 and being rewritten as x14(2+5x12){x}^{\frac{1}{4}}\left(2+5{x}^{\frac{1}{2}}\right)x41(2+5x21). Example 7: Factoring an Expression with Fractional or Negative Exponents Factor 3x(x+2)−13+4(x+2)233x{\left(x+2\right)}^{\frac{-1}{3}}+4{\left(x+2\right)}^{\frac{2}{3}}3x(x+2)3−1+4(x+2)32. Solution Factor out the term with the lowest value of the exponent. In this case, that would be (x+2)−13{\left(x+2\right)}^{-\frac{1}{3}}(x+2)−31. (x+2)−13(3x+4(x+2))Factor out the GCF.(x+2)−13(3x+4x+8)Simplify.(x+2)−13(7x+8)\begin{array}{cc}{\left(x+2\right)}^{-\frac{1}{3}}\left(3x+4\left(x+2\right)\right)\hfill & \text{Factor out the GCF}.\hfill \\ {\left(x+2\right)}^{-\frac{1}{3}}\left(3x+4x+8\right)\hfill & \text{Simplify}.\hfill \\ {\left(x+2\right)}^{-\frac{1}{3}}\left(7x+8\right)\hfill & \end{array}(x+2)−31(3x+4(x+2))(x+2)−31(3x+4x+8)(x+2)−31(7x+8)Factor out the GCF.Simplify. Try It 8 Factor 2(5a−1)34+7a(5a−1)−142{\left(5a - 1\right)}^{\frac{3}{4}}+7a{\left(5a - 1\right)}^{-\frac{1}{4}}2(5a−1)43+7a(5a−1)−41. Solution Licenses & AttributionsCC licensed content, Specific attributionCollege Algebra. Provided by: OpenStax Authored by: OpenStax College Algebra. Located at: https://cnx.org/contents/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1/Preface. License: CC BY: Attribution.