1. Write the problem: Convert $(\sqrt{10})^3$ to exponential form. 2. Recall that $\sqrt{10} = 10^{\frac{1}{2}}$. 3. Use the power of a power rule: $(a^m)^n = a^{m \cdot n}$. 4. Apply the rule: $(\sqrt{10})^3 = (10^{\frac{1}{2}})^3 = 10^{\frac{1}{2} \cdot 3} = 10^{\frac{3}{2}}$. 5. Final answer: $10^{\frac{3}{2}}$.