$$ 7 x^{-\frac{3}{2}} $$ Answer \begin{tabular}{|c|}\hline$$ \frac{7}{\sqrt{x^{3}}} $$ \ $$ \frac{7}{\sqrt[3]{x^{2}}} $$ \ $$ \frac{1}{\sqrt[3]{7 x^{2}}} $$ \ \hline\end{tabular}

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To simplify the expression $$ 7x^{-\frac{3}{2}} $$, let's rewrite it step by step:

1. **Understanding Negative Exponents:**
   
   A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. So,
   
   $$
   x^{-\frac{3}{2}} = \frac{1}{x^{\frac{3}{2}}}
   $$
   
2. **Expressing the Fractional Exponent:**
   
   The exponent $$\frac{3}{2}$$ can be interpreted as the square root of $$x$$ raised to the third power:
   
   $$
   x^{\frac{3}{2}} = \left( \sqrt{x} \right)^3 = \sqrt{x^3}
   $$
   
3. **Combining the Results:**
   
   Substituting back, we get:
   
   $$
   7x^{-\frac{3}{2}} = 7 \times \frac{1}{\sqrt{x^3}} = \frac{7}{\sqrt{x^3}}
   $$

**Therefore, the simplified form of $$ 7x^{-\frac{3}{2}} $$ is:**

$$
\frac{7}{\sqrt{x^{3}}}
$$

Looking at your provided options:

$$
\begin{tabular}{|c|}
\hline
$$ \frac{7}{\sqrt{x^{3}}} $$ \ 
$$ \frac{7}{\sqrt[3]{x^{2}}} $$ \ 
$$ \frac{1}{\sqrt[3]{7 x^{2}}} $$ \ 
\hline
\end{tabular}
$$

**The correct answer is the first option:**

$$
\frac{7}{\sqrt{x^{3}}}
$$
The simplified form of $$ 7x^{-\frac{3}{2}} $$ is $$ \frac{7}{\sqrt{x^{3}}} $$.

\( 7 x^{-\frac{3}{2}} \) Answer \begin{tabular}{|c|}\hline\( \frac{7}{\sqrt{x^{3}}} \) \\ \( \frac{7}{\sqrt[3]{x^{2}}} \) \\ \( \frac{1}{\sqrt[3]{7 x^{2}}} \) \\ \hline\end{tabular}

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