$16^n (mod 9) 7^n$ $16^n+4^n-2 (mod 9) 7^n+4^n-2$ $7^n (mod 9) 7,4,1$ $4^n (mod 9) 4,7,1$ $4^n+7^n (mod 9) 2$

Just check$\pmod 9$ and notice that we obtain $$16^n\equiv(-2)^n\equiv1,-2\text{ or }4\pmod 9\text{ and }4^n\equiv1,4\text{ or }-2\pmod 9\text{ which forces }16^n+4^n\equiv(-2)^n+4^n\equiv 2\pmod 9\text{ thus }16^n+4^n-2\equiv2-2\equiv0\pmod 9$$

yeah just check$mod(9)$