The index (root) of a radical expression refers to the number that indicates the degree of the root. In the given expression, (9^(3/5))^(5/18), we have a nested radical.
To simplify the expression, we can apply the exponent rules. When we raise a power to another power, we multiply the exponents:
(9^(3/5))^(5/18) = 9^((3/5)*(5/18))
Multiplying the exponents, we get:
9^((3/5)*(5/18)) = 9^(15/90)
Simplifying the exponent further, we have:
9^(15/90) = 9^(1/6)
Therefore, the index (root) of the equivalent radical expression is 6.