# Who's up to the challenge? 7

**Algebra**Level 4

You're given that \(\dfrac 1n +\dfrac 1k =1\) and that \(n=4\). If the sum \(\displaystyle\sum _{ i=1 }^{ m }{ { x }_{ i }^{ n } } =1296\) and the sum \(\displaystyle\sum _{ i=1 }^{ m }{ { y }_{ i }^{ k } } =16\) then find the maximum value of \(\displaystyle \sum _{ i=1 }^{ m }{ { x }_{ i }{ y }_{ i } } \).

**Note**: All \({x}_{i}\) and \({y}_{i}\) are non-negative real numbers.

This is a part of Who's up to the challenge?