First this I would like to explain is that ;
[tex] \sqrt{x} = \sqrt[2]{ {x}^{1} } = {x}^{ \frac{1}{2} } [/tex]
This means that when;
[tex] {x}^{ \frac{3}{4} } = \sqrt[4]{ {x}^{3} } [/tex]
either >>
[tex] ({ - 16})^{ \frac{3}{4} } = \sqrt[4]{ { - 16}^{3} } [/tex]
(-16)^3 = -4096
However the 4th root of anything negative is undefined, the answer to your question is undefined.
or >>
[tex] - ( {16}^{ \frac{3}{4} } ) = - \sqrt[4]{ {16}^{ 3 } } = - \sqrt[4]{4096} = - 8[/tex]
