  Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ defined
on $GL_n(\mathbb{A}_E)$ and $GL_m(\mathbb{A}_F)$, respectively, with $E$ and
$F$ solvable algebraic number fields we deduce a prime number theorem for the
Rankin-Selberg L-function $L(s,AI_{E/\mathbb{Q}}(\pi)\times
AI_{F/\mathbb{Q}}(\pi'))$ under a self-contragredient assumption and a suitable
Galois invariance condition on the representations, where $AI_{K/\mathbb{Q}}$
denotes the automorphic induction functor for any number field $K/\mathbb{Q}$.
