How are these two equations the same?

[IntegrateMe]

$$\lim_{n\to\infty}\frac{8^{n-1}}{9^{n}}$$

and

$$\frac{1}{9}\lim_{n\to\infty}(\frac{8}{9})^{n}$$

In particular, why is there a 1/9 beside the limit instead of a 1/8 in the second equation?

 

[Poopsilon]

These are not equations, FYI, they are limits, and as limits they are the same.