Hello Michelle. I can help with some of this.
Principal Root= the non-negative square root of a number. Your problem is 5 raised to the fourth raised to the 1/2. raising a number to the 1/2 is the same as taking the square root. SO you are taking the square root of 5 raised to the fourth. 5 raised to the fourth is 625. The square root of 625 is 25
Product rule=the product rule is a great way to break down numbers that don't actually have square roots. For example, the square root of 8 is equal to the square root of 4 multiplied by the square root of 2 which would be equal to 2√2. In this case, your product rule would give you √5² multiplied by the √5² , which again gives you 25
Quotient rule=n√x multiplied by n√y = n√xy So for your problem,
2√52 multiplied by 2√52 = 2√625
Reciprocal Rule =b√xa = xa/b For your problem
2√54 = 54/2 = 52= 25