Minixima

For non-negative numbers $a$ and $b$ such that their sum is 1, let sum of maximum and minimum value of

$\large { a }^{ 8 }{ b }^{ 3 }+{ a }^{ 3 }{ b }^{ 5 }$

be denoted as $z$ . Evaluate $100z$ to 2 decimal places.

Inspiration .