The expression
[tex]x^{\frac{9}{4}}[/tex]is equivalent to
[tex]\sqrt[4]{x^9}[/tex]then the answer is option D
Since the root and the exponent commute, this also can be written as
[tex](\sqrt[4]{x})^9[/tex]then the answer is option B
And by the same reason, this can be written as
[tex](x^9)^{\frac{1}{4}}[/tex]then the answer is option E