13. Given the sequence $\{\sqrt[n]{n}\}\left(n \in \mathbf{Z}_{+}\right)$. Then the value of the largest term in the sequence is $\qquad$ .
13. $\sqrt[3]{3}$.

Let $f(x)=x^{\frac{1}{x}}=\mathrm{e}^{\frac{1}{x} \ln x}$. Then $f^{\prime}(x)=\frac{x^{\frac{1}{x}}}{x^{2}}(1-\ln x)$.
Solving, we find that $x=\mathrm{e}$ is a point of maximum.
Thus, the largest term in the sequence is the third term, which is $\sqrt[3]{3}$.