If one is six times the other, then you would have 7 equal piles. Divide 105 by 7 to get 15 which is the number in each pile(number of dimes). Then 105 minus 15 gives you the total of the rest of the piles(number of nickels).
The properties of rational exponents can be applied to simplify expressions with radicals or rational exponents by writing radicals as numbers with rational exponents.
That allows you to apply the same properties of rational exponents to them.