4.8 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, [latex]2x^\frac14\;+\;5x^\frac34[/latex] can be factored by pulling out [latex]x^\frac14[/latex] and being rewritten as [latex]x^\frac14(2\;+\;5x^\frac12)[/latex].
Example 1: Factoring an Expression with Fractional or Negative Exponents
- Factor [latex]3x{(x\;+\;2)}^\frac{-1}3\:+\;4{(x\:+\:2)}^\frac23[/latex].
- Factor [latex]2\left(5a-1\right)^\frac{3}{4}+7a\left(5a-1\right)^\frac{-1}{4}[/latex]
Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
