1. **State the problem:** Simplify the expression $$\sqrt{x}20x^2 + \sqrt{x}40x^2$$. 2. **Recall the properties:** The square root of $x$ is written as $\sqrt{x} = x^{\frac{1}{2}}$. 3. **Rewrite the expression using exponents:** $$\sqrt{x}20x^2 + \sqrt{x}40x^2 = 20x^{\frac{1}{2}}x^2 + 40x^{\frac{1}{2}}x^2$$ 4. **Combine the powers of $x$ by adding exponents:** $$20x^{2 + \frac{1}{2}} + 40x^{2 + \frac{1}{2}} = 20x^{\frac{5}{2}} + 40x^{\frac{5}{2}}$$ 5. **Factor out the common term:** $$x^{\frac{5}{2}}(20 + 40) = 60x^{\frac{5}{2}}$$ 6. **Final simplified expression:** $$60x^{\frac{5}{2}}$$