8 dB correspond to a power ratio of ... ?

6.31

Explanation:

Power ratio (in db) = 10 * log [P (out) / P (in) ]

Here, P (in) and P (out) correspond to input and output power in Watts respectively.

This implies, 8 db = 10 * log [P (out) / P (in) ]

Rearranging, log [P (out) / P (in) ] = (8/10)

Or, P (out) / P (in) = 10 ^ 0.8 = 6.31

But, P (out) / P (in) corresponds to the power ratio of output and input power.

So the required power ratio corresponds to 6.31