A common emitter amplifier has a voltage gain of 50 , an input...

Voltage gain $= \beta \times$ impedance gain

$⇒ 50 = \beta \times \dfrac{200}{100}$

$⇒ \beta = 25$

Also power gain $= {\beta}^{2} \times$ impedance gain

$= \left(25\right)^{2} \times \dfrac{200}{100} = 1250$