Use synthetic division to find the function values. $f(x)=x^{4}-16 ;$ find $f(1), f(-1)$ $f(1)=\square$ (Type an exact answer, using radicals as needed) $f(-1)=\square$ (Type an exact answer, using radicals as needed.)

Step 1 ：Substitute $x=1$ into the function $f(x)=x^{4}-16$ to find $f(1)$

Step 2 ：Calculate $f(1)=1^{4}-16=-15$

Step 3 ：Substitute $x=-1$ into the function $f(x)=x^{4}-16$ to find $f(-1)$

Step 4 ：Calculate $f(-1)=(-1)^{4}-16=-15$

Step 5 ：So, $f(1)=\boxed{-15}$ and $f(-1)=\boxed{-15}$