1. **State the problem:** Simplify the expression $$\left(\frac{x^3}{x^{\frac{1}{2}}}\right) \times \left(\frac{x^{\frac{3}{2}}}{x^0}\right) \times x^7$$. 2. **Recall the laws of exponents:** - When dividing powers with the same base, subtract exponents: $$\frac{x^a}{x^b} = x^{a-b}$$. - When multiplying powers with the same base, add exponents: $$x^a \times x^b = x^{a+b}$$. - Any number to the zero power is 1: $$x^0 = 1$$. 3. **Simplify each part:** - First part: $$\frac{x^3}{x^{\frac{1}{2}}} = x^{3 - \frac{1}{2}} = x^{\frac{6}{2} - \frac{1}{2}} = x^{\frac{5}{2}}$$. - Second part: $$\frac{x^{\frac{3}{2}}}{x^0} = x^{\frac{3}{2} - 0} = x^{\frac{3}{2}}$$. 4. **Combine all parts:** $$x^{\frac{5}{2}} \times x^{\frac{3}{2}} \times x^7 = x^{\frac{5}{2} + \frac{3}{2} + 7}$$. 5. **Add the exponents:** $$\frac{5}{2} + \frac{3}{2} + 7 = \frac{5+3}{2} + 7 = \frac{8}{2} + 7 = 4 + 7 = 11$$. 6. **Final simplified expression:** $$x^{11}$$. **Answer:** C $x^{11}$