For a, b, c > 0

What is lim (n-->infinity){ [a^(1/n)+b^(1/n)+c^(1/n)]/3}^n equal to ?

The limit converges, as I have tried to similuate the number. The answer must be in terms of a, b, and c.

I tried to expand by binomial series, but got to nowhere useful.

If anyone could help, I would be appreciated. Thank you very much.