1. The problem is to simplify the expression $10x^2 \sqrt{x}$. 2. Recall that $\sqrt{x} = x^{\frac{1}{2}}$. 3. Rewrite the expression using exponents: $$10x^2 \sqrt{x} = 10x^2 x^{\frac{1}{2}}$$ 4. Use the rule of exponents that states $a^m \cdot a^n = a^{m+n}$ to combine the powers of $x$: $$10x^{2 + \frac{1}{2}} = 10x^{\frac{4}{2} + \frac{1}{2}} = 10x^{\frac{5}{2}}$$ 5. The simplified form of the expression is $$10x^{\frac{5}{2}}$$. This means the expression is $10$ times $x$ raised to the power $\frac{5}{2}$.