I am not sure what you mean by the symbol ^, we use this symbol to express the power, but in your question there is no base . So I will assume the following:
3sqrt(a) * 5sqrt(a)
Multiply integers together and square roots together.
= (3*5)* (sqrt(a)*sqrt(a))
= 15 (a)
= 15 a
Hope you mean to somplify *sqrt(a))^3*(sqrt(a))^3
(sqrt(a))^3*(sqrt(a))^5 = (a^(1/2))^3 * (a^(1/2))^5
= (a^(3/2))(a^5/2), as (a^m)^n a^(mn).
= a^(3/2+5/2), as (a^m)(a^n) = a^(m+n).