Answer
$\{ -239, 247\}$
Work Step by Step
Step 1. Given $(x-4)^{2/5}=9$, raise both side to the 5th power, we have $(x-4)^{2}=9^5=3^{10}$
Step 2. Take square root on both sides to get $x-4=\pm(3^5)=\pm243$
Step 3. Thus $x=-239, 247$ or in set form $\{ -239, 247\}$
