1. The problem is to simplify the expression $\frac{8!}{7!}$.\n\n2. Recall the definition of factorial: for any positive integer $n$, $n! = n \times (n-1) \times (n-2) \times \cdots \times 1$.\n\n3. Using this, $8! = 8 \times 7!$.\n\n4. Substitute $8!$ in the expression: $$\frac{8!}{7!} = \frac{8 \times 7!}{7!}.$$\n\n5. Since $7!$ appears in both numerator and denominator, they cancel out: $$\frac{8 \times 7!}{7!} = 8.$$\n\n6. Therefore, the simplified value of $\frac{8!}{7!}$ is $8$.