The problem is to simplify the expression $\frac{5^7}{5^8}$.

1. Problem Description

The problem is to simplify the expression $\frac{5^7}{5^8}$.

2. Solution Steps

To simplify the expression $\frac{5^7}{5^8}$, we can use the property of exponents:

$\frac{a^m}{a^n} = a^{m-n}$

Applying this property, we have:

$\frac{5^7}{5^8} = 5^{7-8} = 5^{-1}$

We also know that $a^{-n} = \frac{1}{a^n}$, so

$5^{-1} = \frac{1}{5^1} = \frac{1}{5}$.

3. Final Answer

$\frac{1}{5}$