1. **Stating the problem:** Simplify the expression $x\sqrt{x}$. 2. **Recall the rule:** The square root of $x$ is $\sqrt{x} = x^{\frac{1}{2}}$. 3. **Rewrite the expression:** $$x\sqrt{x} = x \cdot x^{\frac{1}{2}}$$ 4. **Use the property of exponents:** When multiplying powers with the same base, add the exponents: $$x^{1} \cdot x^{\frac{1}{2}} = x^{1 + \frac{1}{2}} = x^{\frac{3}{2}}$$ 5. **Final answer:** $$x\sqrt{x} = x^{\frac{3}{2}}$$ This means the expression simplifies to $x$ raised to the power of $\frac{3}{2}$, which is a more compact and useful form for further calculations.