If $8^{-x}=13$, what does $8^{2 x}$ equal?

Step 1 ：The given equation is \(8^{-x}=13\). We need to find the value of \(8^{2x}\). We know that \(8^{2x} = (8^x)^2\). If we can find the value of \(8^x\), we can square it to get the value of \(8^{2x}\).

Step 2 ：From the given equation, we can express \(8^x\) in terms of 13. Since \(8^{-x}=13\), we can write \(8^x = 1/13\).

Step 3 ：So, \(8^{2x} = (8^x)^2 = (1/13)^2\).

Step 4 ：Let's calculate this. The result is 0.00591715976331361.

Step 5 ：Final Answer: The value of \(8^{2x}\) is \(\boxed{0.00591715976331361}\).