Question Number 121170 by pooooop last updated on 05/Nov/20
$$\:\:\:\:\:\:\left(\boldsymbol{{a}};\boldsymbol{{b}};\boldsymbol{{c}}\right)\in\forall \\ $$$$\:\boldsymbol{{a}}^{\boldsymbol{{a}}} \centerdot\:\boldsymbol{{b}}^{\boldsymbol{{b}}} \centerdot\:\boldsymbol{{c}}^{\boldsymbol{{c}}} \geqslant\left(\boldsymbol{{abc}}\right)^{\frac{\boldsymbol{{a}}+\boldsymbol{{b}}+\boldsymbol{{c}}}{\mathrm{3}}} \\ $$