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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: $3^{2} \times 7^{2} \times 8^{2}=28224$
$=\frac{1}{28224}$
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