The problem is to divide the polynomial $-21a^2b^3 + 21ab^3 - 7ab^2$ by the monomial $7ab^2$. We need to simplify the resulting expression.

1. Problem Description

The problem is to divide the polynomial $-21a^2b^3 + 21ab^3 - 7ab^2$ by the monomial $7ab^2$. We need to simplify the resulting expression.

2. Solution Steps

First, we write the expression as a fraction:

$\frac{-21a^2b^3 + 21ab^3 - 7ab^2}{7ab^2}$

Then, we divide each term in the numerator by the denominator:

$\frac{-21a^2b^3}{7ab^2} + \frac{21ab^3}{7ab^2} - \frac{7ab^2}{7ab^2}$

Now we simplify each term:

$\frac{-21a^2b^3}{7ab^2} = -3ab$

$\frac{21ab^3}{7ab^2} = 3b$

$\frac{7ab^2}{7ab^2} = 1$

Finally, we combine the simplified terms:

$-3ab + 3b - 1$

3. Final Answer

The final answer is $-3ab + 3b - 1$.