1. The problem is to simplify the expression $\sqrt{x}$ raised to the power 3. 2. We start with the expression $\left(\sqrt{x}\right)^3$. 3. Recall that $\sqrt{x} = x^{\frac{1}{2}}$. So the expression becomes $\left(x^{\frac{1}{2}}\right)^3$. 4. Use the power of a power property of exponents: $\left(a^m\right)^n = a^{mn}$. Therefore, $\left(x^{\frac{1}{2}}\right)^3 = x^{\frac{1}{2} \times 3}$. 5. Multiply the exponents: $\frac{1}{2} \times 3 = \frac{3}{2}$. So the expression simplifies to $x^{\frac{3}{2}}$. 6. Therefore, $\left(\sqrt{x}\right)^3 = x^{\frac{3}{2}}$.