Rule # 1- If a variable has an even numbered exponent, divide the exponent by 2 and pull it out of the radical.

 

Example

=

 

4 divided by 2 = 2

 

 

 

Example

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14 divided by 2 = 7.

 

 

Rule # 2- If the variable has an odd exponent, then rewrite it as a product with an even numbered exponent. Apply Rule # 1 to the even exponent.

 

 

 

Example

 

 

 

Rewrite as even numbered exponent. =.

 

=

 

Answer!

 

 

 

 

Example

 

 

Rewrite as even numbered exponent=

 

 

=

 

 

Answer!

 

Now combine the perfect squares and the two rules of variables.

 

 

 

 

Example

 

 

32 can be written as 16(2) and x² is already an even numbered exponent.

 

= and = .

 

Answer!

 

 

 

 

 

Example

 

 

150 can be written as 25(6). And =.

 

 

= and = . Combine what is left under the radical (6 and y) into one radical.

 

Answer!

 

 

 

 

Example

 

162 can be written as 81(2). = and =

 

 

 

= and = . Combine what is left underneath the radicals (2 and x) into a single radical.

 

 

 

Answer!