The power gain of an amplifier can be calculated using the formula:

Power Gain (dB) = 10 * log10(Pout / Pin)

where Pout is the output power and Pin is the input power.

In this case, we are given the voltage gain (AV) and current gain (AI) of the amplifier. The power gain can be calculated using the following relation:

Power Gain = AV * AI

Given that the voltage gain is 8 and the current gain is 7, we can calculate the power gain as:

Power Gain = 8 * 7 = 56

Now, let's calculate the power gain in dB:

Power Gain (dB) = 10 * log10(56) ≈ 17.481 dB

Therefore, the correct answer is option B: 17.481 dB.

Explanation in Detail:

1. Voltage Gain (AV):
The voltage gain of an amplifier is the ratio of the output voltage to the input voltage. It indicates how much the amplifier amplifies the input voltage signal. In this case, the voltage gain is given as 8.

2. Current Gain (AI):
The current gain of an amplifier is the ratio of the output current to the input current. It indicates how much the amplifier amplifies the input current signal. In this case, the current gain is given as 7.

3. Power Gain:
The power gain of an amplifier is the ratio of the output power to the input power. It indicates how much the amplifier amplifies the input power signal. The power gain can be calculated by multiplying the voltage gain and current gain together.

4. Calculation of Power Gain:
Given that the voltage gain is 8 and the current gain is 7, we can calculate the power gain as:

Power Gain = Voltage Gain * Current Gain
Power Gain = 8 * 7
Power Gain = 56

5. Calculation of Power Gain in dB:
The power gain in dB can be calculated using the formula:

Power Gain (dB) = 10 * log10(Power Gain)

Substituting the value of Power Gain, we get:

Power Gain (dB) = 10 * log10(56)
Power Gain (dB) ≈ 17.481 dB

Therefore, the power gain of the amplifier is approximately 17.481 dB.