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 √5^{² }multiplied by the √5² , which again gives you 25

Quotient rule=^{n}√x multiplied by ^{n}√y = ^{n}√xy So for your problem,
^{2}√5^{2 }multiplied by ^{2}√5^{2 }= ^{2}√625

Reciprocal Rule =^{b}√x^{a = }x^{a/b} For your problem
^{2}√5^{4 }= 5^{4/2} = 5^{2}= 25

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