9. Expressed as a radical expression, the fraction $$ \frac{x^{1 / 3} x^{1 / 2}}{x^{-1}} $$ is $$ \begin{array}{ll} ext { (1) } \frac{1}{\sqrt[6]{x}} & ext { (3) } \sqrt[11]{x^{6}} \ ext { (2) } \frac{1}{\sqrt[11]{x^{6}}} & ext { (4) } \sqrt[6]{x^{11}}\end{array} $$

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9. Expressed as a radical expression, the fraction $$ \frac{x^{1 / 3} x^{1 / 2}}{x^{-1}} $$ is $$ \begin{array}{ll}	ext { (1) } \frac{1}{\sqrt[6]{x}} & 	ext { (3) } \sqrt[11]{x^{6}} \ 	ext { (2) } \frac{1}{\sqrt[11]{x^{6}}} & 	ext { (4) } \sqrt[6]{x^{11}}\end{array} $$

UpStudy AI · Accepted Answer

To simplify the expression $$\frac{x^{1/3} x^{1/2}}{x^{-1}}$$ and express it as a radical expression, follow these steps:

1. **Combine the exponents in the numerator:**
   $$
   x^{1/3} \cdot x^{1/2} = x^{1/3 + 1/2} = x^{5/6}
   $$

2. **Divide by $$x^{-1}$$:**
   $$
   \frac{x^{5/6}}{x^{-1}} = x^{5/6 - (-1)} = x^{5/6 + 1} = x^{11/6}
   $$

3. **Express $$x^{11/6}$$ as a radical:**
   $$
   x^{11/6} = \sqrt[6]{x^{11}}
   $$

Therefore, the expression $$\frac{x^{1/3} x^{1/2}}{x^{-1}}$$ written as a radical is:

**Answer:** (4) $$\sqrt[6]{x^{11}}$$
The expression simplifies to $$ \sqrt[6]{x^{11}} $$, which is option (4).

Expressed as a radical expression, the fraction is

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