10. (2006 National High School Mathematics League Zhejiang Preliminary Contest Question) $\max _{a, b, \cdots \in \mathbf{R}^{+}} \min \left\{\frac{1}{a}, \frac{1}{b^{2}}, \frac{1}{c^{3}}, a+b^{2}+c^{3}\right\}=$