Given: Voltage gain, $A_v = 50$ Input impedance, $R_i = 100 \text{ } \Omega$ Output impedance, $R_o = 200 \text{ } \Omega$

The power gain ($A_p$) of an amplifier is given by the ratio of output power to input power: $A_p = \frac{P_{out}}{P_{in}} = \frac{V_{out}^2 / R_o}{V_{in}^2 / R_i} = \left(\frac{V_{out}}{V_{in}}\right)^2 \times \frac{R_i}{R_o}$ Since $A_v = \frac{V_{out}}{V_{in}}$, we have: $A_p = A_v^2 \times \frac{R_i}{R_o}$

Substituting the given values: $A_p = (50)^2 \times \frac{100}{200}$ $A_p = 2500 \times \frac{1}{2} = 1250$

Alternatively, we can first find the current gain ($\beta$): $A_v = \beta \times \frac{R_o}{R_i}$ $50 = \beta \times \frac{200}{100} \implies \beta = 25$

Then, Power Gain = Voltage Gain $\times$ Current Gain: $A_p = A_v \times \beta = 50 \times 25 = 1250$