Evaluate :  $ \left(3^{-2} \times 7^{-2}\right) \times 8^{-2} $

We have to simplify: $\left(3^{-2} \times 7^{-2}\right) \times 8^{-2}$

Apply exponent rule: $a^{-b}=\frac{1}{a^{b}}$

$=\frac{1}{3^{2}} \times \frac{1}{7^{2}} \times \frac{1}{8^{2}}$

Multiply fractions:

$=\frac{1 \times 1 \times 1}{3^{2} \times 7^{2} \times 8^{2}}$

$=\frac{1}{3^{2} \times 7^{2} \times 8^{2}}$

By multiplying we can calculate: $3^{2} \times 7^{2} \times 8^{2}=28224$

$=\frac{1}{28224}$