Annual roots 1

The graph of $x^{2015}$ will be alike $x^3$ with range ( $-\infty,+\infty$ ) ,so it will cut line y=2015 only once,hence it has 1 solution.

Since the derivative of this function is $f'(x)=2015x^{2014}$ .

So, this implies that this function is an increasing function(only have a stationary point at x=0)

Hence, it's a one-to-one function and have only 1 real root.

Lemma : $x^{2k+1} = a \Rightarrow x = \sqrt[2k+1]{a}$ for every integer $k$ $x \in \mathbb{R} \quad \& \quad x^{2015} = 2015 \Rightarrow \boxed{x =\sqrt[2015]{2015} } \rightarrow$ 1 real root.