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.

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