To simplify the expression \( x^{\frac{3}{4}} \), we can interpret this in terms of exponents and roots.
The expression \( x^{\frac{3}{4}} \) can be rewritten using the properties of exponents as follows:
\[ x^{\frac{3}{4}} = \sqrt[4]{x^3} \]
This means that \( \sqrt[4]{x^3} \) is equivalent to \( x^{\frac{3}{4}} \).
Now let's evaluate the provided options:
- \( \sqrt[4]{x} \) (this is \( x^{\frac{1}{4}} \))
- \( \frac{1}{\sqrt[4]{x}} \) (this is \( x^{-\frac{1}{4}} \))
- \( x \) (this is \( x^{1} \))
- \( x^{4} \) (this is \( x^{4} \))
None of these options directly match \( x^{\frac{3}{4}} \). However, the closest correct interpretation is:
\( \sqrt[4]{x^3} \) (not listed as an option)
But if I must select one from your list, none of the options are equivalent to \( x^{\frac{3}{4}} \). Please check for potential typos or additional options.