On factorizations into coprime parts

Let $f(n)$ and $g(n)$ be the number of unordered and ordered factorizations of $n$ into integers larger than one. Let $F(n)$ and $G(n)$ have the additional restriction that the factors are coprime. We establish the asymptotic bounds for the sums of $F(n)^{beta}$ and $G(n)^{beta}$ up to $x$ for all real $beta$ and the asymptotic bounds for $f(n)^{beta}$ and $g(n)^{beta}$ for all negative $beta$.