amplifier question

Power is proportional to the square of the voltage.
W = V*V/R

 

Here is a good example as why you should not be looking for a formula.
Lest's take the givens. The author makes a very big mistake by not clearly defining the parameters so we'll make assumptions based on what is given.
We will assume the input impedance is 600 ohms and the load of the amplifier is 600 ohms.
We will also assume that the voltage on the load resistor is 10 volts.
Now we have a ratio, the output power and the input power.
The power being power being dissipated by a resistor is directly proportional to the voltage times the current going through the resistor and the current is directly proportional to the voltage across the resistor. Therefore the power is directly proportional to the voltage squared.

The output voltage is 10 volts.
The input voltage is ?
The power gain is 25.

So what ratio of voltages will produce a power ratio of 25?

The input voltage is driving 600 ohms.
10 volts is driving output load resistor of 600 ohms.

I just gave you all the information needed to solve this problem.
I did not give you a formula.

My main point of answering this blog is to tell you and everybody else to not look to formulas. If you cannot derive a formula do not use it. This is about the worst thing you can do.
Only solve problems based on the science or the physics and definitions.

You may have been confused by the terrible way the author defined his parameters so that forces you to come up with assumptions. But even if you do not get the book answer you have a fighting chance arguing with your professor as long as you can clearly demonstrate your chain of logic.