The properties of radicals are based on the Exponentiation Rules.

1.  If the index  k  is the reciprocal of a natural number  n,   k = 1 / n, then
   
   
   ,
   
   where  a  and  b  are assumed to be non-negative numbers.
   Therefore,
   
   

   The product of the  nth roots of real numbers is equal to the  nth root of the product of the numbers.

   
   
   
2. Likewise, if  b ≠ 0  then
   
   .
   
   
   

   The quotient of the  nth roots of real numbers is equal to the  nth root of the quotient of the numbers.

   
   
   
3. For any non-negative integer  a,
   
   
   .
   
   

   To raise to a power the  nth roots of a real number, raise to the power the radicand.

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