The n-th root of x is equivalent to raising x to the power of 1/n, so
[tex]2\sqrt[4]{x^7} = 2\left(x^7\right)^{1/4}[/tex]
If you raise x to some power n, then raise that to another power m, the result is raising x to the power of mn, so
[tex]2\left(x^7\right)^{1/4} = \boxed{2x^{7/4}}[/tex]
