The problem is to calculate $\frac{8}{7} \div \frac{2}{35}$ and express the answer in its simplest form.

1. Problem Description

The problem is to calculate $\frac{8}{7} \div \frac{2}{35}$ and express the answer in its simplest form.

2. Solution Steps

To divide fractions, we multiply by the reciprocal of the second fraction. The reciprocal of $\frac{2}{35}$ is $\frac{35}{2}$. So we have

$$\frac{8}{7} \div \frac{2}{35} = \frac{8}{7} \times \frac{35}{2}$$

Multiplying the numerators and denominators:

$$\frac{8}{7} \times \frac{35}{2} = \frac{8 \times 35}{7 \times 2}$$

$$= \frac{280}{14}$$

Now we simplify the fraction.

First, we can divide both numerator and denominator by 2:

$$\frac{280}{14} = \frac{140}{7}$$

Then, we can divide both numerator and denominator by 7:

$$\frac{140}{7} = \frac{20}{1}$$

$$= 20$$

3. Final Answer

20