# An algebra problem by shubham dhull

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 $$a + b +c$$.

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