## a^{b+c} + b^{c+a} + c^{a+b} ≤ 1

If   $a, \; b, \; c$   are positive real numbers such that   $a \, b \, c \; = \; 1$ ,

prove that

$a^{b+c} \; + \; b^{c+a} \; + \; c^{a+b} \; \leq \; 1$