Rewrite the following radical expression in rational exponent form. $$ (\sqrt{x})^{5} $$ A. $$ \frac{x^{3}}{x^{5}} $$ B. $$ \left(\frac{1}{x^{2}}\right)^{5} $$ C. $$ x^{\frac{5}{6}} $$ D. $$ x^{\frac{5}{2}} $$

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To rewrite the radical expression $$(\sqrt{x})^{5}$$ in rational exponent form, follow these steps:

1. **Understand the Radical**:
   - The square root of $$x$$ can be expressed as a fractional exponent:
     $$
     \sqrt{x} = x^{\frac{1}{2}}
     $$

2. **Apply the Exponent**:
   - Raise $$x^{\frac{1}{2}}$$ to the 5th power:
     $$
     \left(x^{\frac{1}{2}}\right)^{5}
     $$

3. **Use the Power of a Power Rule**:
   - When raising a power to another power, multiply the exponents:
     $$
     x^{\frac{1}{2} \times 5} = x^{\frac{5}{2}}
     $$

So, the expression $$(\sqrt{x})^{5}$$ written in rational exponent form is:

$$
x^{\frac{5}{2}}
$$

**Answer:**  
D. $$ x^{\frac{5}{2}} $$
The answer is $$ x^{\frac{5}{2}} $$, choice D.

Rewrite the following radical expression in rational exponent form. \[ (\sqrt{x})^{5} \] A. \( \frac{x^{3}}{x^{5}} \) B. \( \left(\frac{1}{x^{2}}\right)^{5} \) C. \( x^{\frac{5}{6}} \) D. \( x^{\frac{5}{2}} \)

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