An algebra problem by Brilliant Member

Algebra Level 4

\[\large \prod_{n=1}^\infty (3^n)^{1/3^n} =3^{1/3} \times 9^{1/9} \times 27^{1/27} \times \cdots \]

The product above can be expressed as \( a^{b/c} \), where \(a\) is a prime number, and \(b,c\) are coprime positive integers. Find \( a + b +c\).