Simplify the algebraic expression: $(-3a)^2 \times 2b \div \frac{6}{7}ab$.

1. Problem Description

Simplify the algebraic expression: $(-3a)^2 \times 2b \div \frac{6}{7}ab$.

2. Solution Steps

First, we evaluate the power:

$(-3a)^2 = (-3)^2 \times a^2 = 9a^2$.

So the expression becomes:

$9a^2 \times 2b \div \frac{6}{7}ab$.

Next, we perform the multiplication:

$9a^2 \times 2b = 18a^2b$.

Then, we have:

$18a^2b \div \frac{6}{7}ab$.

To divide by a fraction, we multiply by the reciprocal of the fraction:

$18a^2b \times \frac{7}{6ab}$.

Now, we multiply the terms:

$\frac{18a^2b \times 7}{6ab} = \frac{126a^2b}{6ab}$.

Finally, we simplify the fraction by canceling common factors:

$\frac{126}{6} \times \frac{a^2}{a} \times \frac{b}{b} = 21 \times a \times 1 = 21a$.

3. Final Answer

The simplified expression is $21a$.