Express \( x^{\frac{3}{4}} \) in terms of a radical expression.

To express \( x^{\frac{3}{4}} \) as a radical, you can use the relationship between exponents and roots. The general form is: \[ x^{\frac{a}{b}} = \sqrt[b]{x^a} \] Applying this to \( x^{\frac{3}{4}} \): \[ x^{\frac{3}{4}} = \sqrt[4]{x^3} \] **Alternative Forms:** 1. **Inside the Radical:** \[ \sqrt[4]{x^3} \] This represents the fourth root of \( x^3 \). 2. **Outside the Radical:** \[ \left( \sqrt[4]{x} \right)^3 \] This represents the cube of the fourth root of \( x \). Both forms are mathematically equivalent and correct. You can choose either based on the context or preference. **Final Answer:** \[ x^{\frac{3}{4}} = \sqrt[4]{\,x^{\,3\,}} \]