Limit of $x^ny^n$ when $n \to \infty$ Please, someone could help me in solving the following limit. 

Let $x \in \mathbb{R}$, $y \in \mathbb{R}$ and $n \in \mathbb{N}$. Also consider that $0&lt;x&lt;1$ and $1&lt;y&lt;\infty$. 

$$ \lim_{n \to \infty}x^ny^n = L $$.

What is the value of $L$ ?
$$x^ny^n = (xy)^n$$

If $xy&lt;1$ , Limit = $0$

If $xy=1$, Limit = 1

If $xy&gt;1$, Limit $\to \infty$
$L=\infty$ since the function is in form $\frac{\infty}{0}$ where $n\to \infty$