Simplify the expression $\frac{7a^8}{7a}$ and express the answer using positive exponents.

1. Problem Description

Simplify the expression $\frac{7a^8}{7a}$ and express the answer using positive exponents.

2. Solution Steps

To simplify the given expression $\frac{7a^8}{7a}$, we can divide the coefficients and use the quotient rule for exponents.

The quotient rule for exponents states that when dividing exponential expressions with the same base, we subtract the exponents:

$\frac{x^m}{x^n} = x^{m-n}$.

In the given expression, we have:

$\frac{7a^8}{7a} = \frac{7}{7} \cdot \frac{a^8}{a^1}$

Since $\frac{7}{7} = 1$, the expression becomes:

$1 \cdot \frac{a^8}{a^1} = \frac{a^8}{a^1}$.

Applying the quotient rule for exponents, we get:

$a^{8-1} = a^7$.

3. Final Answer

$a^7$