Factoring an Expression with Fractional or Negative Exponents

Factor $3 x {(x + 2)}^{\frac{−1}{3}} + 4 {(x + 2)}^{\frac{2}{3}} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Factor out the term with the lowest value of the exponent. In this case, that would be ${(x + 2)}^{- \frac{1}{3}} .$

$\begin{matrix} {(x + 2)}^{- \frac{1}{3}} (3 x + 4 (x + 2)) & Factor out the GCF . \\ {(x + 2)}^{- \frac{1}{3}} (3 x + 4 x + 8) & Simplify . \\ {(x + 2)}^{- \frac{1}{3}} (7 x + 8) \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Factor $2 {(5 a - 1)}^{\frac{3}{4}} + 7 a {(5 a - 1)}^{- \frac{1}{4}} .$

How did it go?