The thought behind this is that we are looking for the square root of . This means that we are looking for an expression that, when we square it, we get . 

What do you think it is?

Let's find out if you are right:

Since   squared is ,is the square root of 
 

The thought behind this is that we are looking for the cube root of . This means that we are looking for an expression that, when we cube it, we get .

What do you think it is?
 
 

Let's find out if you are right:

Since   cubed is , is the cube root of . 
 

The thought behind this is that we are looking for the fourth root of . This means that we are looking for an expression that, when we raise it to the fourth power,  we get .

What do you think it is?
 
 

Let's find out if you are right:

Since   raised to the fourth power is  and there is a negative in front of the radical, is the negative fourth root of . 
 

The thought behind this is that we are looking for the fifth root of   .  This means that we are looking for an expression that, when we raise it to the fifth power, we get  . 

What do you think it is?

Let's find out if you are right:

Since  raised to the fifth power  is  ,   is the fifth root of . 
 

Since it didn't say that x or y are positive, we have to assume that they can be either positive or negative.  Since the root number and exponent are equal, then we can use the rule.

Since the root number and the exponent inside are equal and are the even number 2, then we need to put an absolute value around x - y for our answer.  The reason for the absolute value is that we do not know if x or y are positive or negative.  So if we put x - y as our answer and it was negative, it would not be a true statement.

Since the root number and exponent are equal then we can use the rule.

This time our root number and exponent were both the odd number 3.  When an odd numbered root and exponent match, then the answer is the base whether it is negative or positive..