The given expression is:
[tex] \sqrt[4]{ 9^{ \frac{1}{2}x } } [/tex]
4th root is equivalent to raising the expression to power [tex] \frac{1}{4} [/tex]. So, re-writing the expression by converting radical to exponent:
[tex] ( 9^{ \frac{1}{2}x } )^{ \frac{1}{4} } \\ \\
= 9^{ \frac{1}{8}x } [/tex]
Therefore, the given expression simplifies to [tex]9^{ \frac{1}{8}x } [/tex]
