Answer
$\{ \pm2, \pm 3, \pm 2i \}$
Work Step by Step
Step 1. Factor the polynomial $f(x)=x^4(x^2-9)-16(x^2-9)=(x^2-9)(x^4-16)=(x^2-9)(x^2-4)(x^2+4)$
Step 2. For $x^2-9=0$, we have $x=\pm 3$
Step 3. For $x^2-4=0$, we have $x=\pm 2$
Step 4. For $x^2+4=0$, we have $x=\pm 2i$
Step 5. The zeros are $\{ \pm2, \pm 3, \pm 2i \}$