Add or subtract terms whenever possible: 2 times the fifth root of 4 plus 5 times the fifth root of 4.

Step-by-step solution

1. 1

   Check whether the radicals are alike. Two radical terms combine only when the index and the radicand both match. Here both are fifth roots of $4$, so they are like radicals.

2. 2

   Treat the radical as a single symbol. Writing $r = \sqrt[5]{4}$ turns the problem into $2r + 5r$, which is ordinary like-term collection.

3. 3

   Add the coefficients. $2 + 5 = 7$, so the sum is $7r$.

4. 4

   Restore the radical and check it cannot be simplified. $4 = 2^2$ contains no perfect fifth power, so $\sqrt[5]{4}$ is already in lowest terms and the answer is $7\sqrt[5]{4}$.

5. 5

   Check numerically. $\sqrt[5]{4} \approx 1.319508$, so the left side is $2(1.319508) + 5(1.319508) \approx 9.23655$ and $7(1.319508) \approx 9.23655$.