Given: x^x= 1/(3^1/9), find the value of: 81x^2 + 1/3x =?

I suspect a typo, since x^x is a rather intractable function, and

1/3^(1/9) does not resolve into anything of that form.

81x^2 + 1/3x = 81x^2 + (1/27)x = 81x^2 + (x^(1/9))/27 = 81x^2 + (1/3^1/9)/27 = 81x^2 + 1/3