To simplify the expression [tex]\(\frac{x}{x^{\frac{3}{4}}}\)[/tex], we can use the properties of exponents. Here's a step-by-step solution:
1. Recall the property of exponents: [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex].
2. Apply this property to the expression [tex]\(\frac{x}{x^{\frac{3}{4}}}\)[/tex]:
[tex]\[
\frac{x}{x^{\frac{3}{4}}} = x^{1 - \frac{3}{4}}
\][/tex]
3. Simplify the exponent:
[tex]\[
1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}
\][/tex]
4. So, [tex]\(\frac{x}{x^{\frac{3}{4}}}\)[/tex] simplifies to:
[tex]\[
x^{\frac{1}{4}}
\][/tex]
The expression [tex]\(x^{\frac{1}{4}}\)[/tex] is equivalent to [tex]\(\sqrt[4]{x}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\sqrt[4]{x}
\][/tex]
