Calculate the power out put of an amplifier that has an input of 15 μw and a gain of 25dB?

If you want to work in watts, convert 25dB to a scalling factor:

3dB = 2 x input

10dB = 10 x input

20dB = 100 x input

...25dB = 10 ^ (25/10) = 316.2 x input

So the output is 15 micro Watts x 316.2 = (4700)/(10^6) = 4.7 milli watts

If you want to work in dB, then convert 15 micro watts to dB:

10 * log |P| = dB = 10*log |15 x 10^6| = -48.2dB

***When you have very small (ie negative) dB, it is often referred to in dBm, or 1/1000 of dB ( 30 dBm = 0 dB)

so the output is -18.2dBm + 25 = 6.8dBm, or -23.2dB