An algebra problem by Brilliant Member

Algebra Level 4

n=1(3n)1/3n=31/3×91/9×271/27×\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 ab/c a^{b/c} , where aa is a prime number, and b,cb,c are coprime positive integers. Find a+b+c a + b +c.

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