1. **State the problem:** Simplify the expression $\sqrt{x}x^2 - 3x$. 2. **Recall the rules:** - $\sqrt{x}$ is the same as $x^{\frac{1}{2}}$. - When multiplying powers with the same base, add the exponents: $x^a \cdot x^b = x^{a+b}$. 3. **Simplify the first term:** $$\sqrt{x}x^2 = x^{\frac{1}{2}} \cdot x^2 = x^{\frac{1}{2} + 2} = x^{\frac{1}{2} + \frac{4}{2}} = x^{\frac{5}{2}}$$ 4. **Rewrite the expression:** $$x^{\frac{5}{2}} - 3x$$ 5. **Express the second term with the same base exponent format:** $$3x = 3x^1$$ 6. **Final simplified expression:** $$x^{\frac{5}{2}} - 3x^1$$ This is the simplified form; the terms cannot be combined further because they have different exponents.