Annual roots 2

The graph of $x^{2016}$ will be alike $x^3$ with range [ $0,+\infty$ ) ,so it will cut line y=2016 twice,hence it has 2 solution.

Lemma : $x^{2k} = a \Rightarrow x = \pm \sqrt[2k]{a}$ for every integer $k$

$x \in \mathbb{R} \quad \& \quad x^{2016} = 2016 \Rightarrow \boxed{x = \pm \sqrt[2016]{2016} } \rightarrow$ 2 real roots.