We are asked to evaluate the expression $\frac{1}{8^3} \times \frac{1}{25^2}$.

1. Problem Description

We are asked to evaluate the expression $\frac{1}{8^3} \times \frac{1}{25^2}$.

2. Solution Steps

First, we evaluate $8^3$.

$8^3 = 8 \times 8 \times 8 = 64 \times 8 = 512$

Next, we evaluate $25^2$.

$25^2 = 25 \times 25 = 625$

Now, we have $\frac{1}{512} \times \frac{1}{625}$.

Multiply the numerators and the denominators:

$\frac{1 \times 1}{512 \times 625} = \frac{1}{320000}$

3. Final Answer

$\frac{1}{320000}$