1. C.
The rule of powers is that when a parenthesis is raised to a power, you multiply the two numbers. Since it is being raised to the second power, it needs to have a 10 in the parenthesis. That would make 20.
2. B
Firstly 10^2 = 100, so we know that the number must be 10. That leaves us with just A and B. Then we know the same thing from the previous equation, that they need to be multiplied together.