Let f(x)=`sqrt(x^5)` then f(5x) is equal to:

Options

A. 5x`sqrt(5x)`
B. `25x^2sqrt(5x)`
C. 5x
D. `sqrt(5x^5)`

Answer

To solve the problem, we need to evaluate \( f(5x) \) given that \( f(x) = \sqrt{x^5} \).

### Step-by-Step Solution:

1. **Define the function**: We start with the function given in the problem:
\[ f(x) = \sqrt{x^5} \]

2. **Simplify the function**: We can rewrite \( \sqrt{x^5} \) using the properties of exponents:
\[ f(x) = \sqrt{x^5} = x^{5/2} \]

3. **Substitute \( 5x \) into the function**: Now, we need to find \( f(5x) \):
\[ f(5x) = (5x)^{5/2} \]

4. **Apply the exponent**: We can apply the exponent to both the 5 and \( x \):
\[ f(5x) = 5^{5/2} \cdot x^{5/2} \]

5. **Simplify \( 5^{5/2} \)**: The term \( 5^{5/2} \) can be rewritten as:
\[ 5^{5/2} = 5^2 \cdot \sqrt{5} = 25\sqrt{5} \]

6. **Combine the results**: Now we can combine everything:
\[ f(5x) = 25\sqrt{5} \cdot x^{5/2} \]

7. **Express in a standard form**: We can express \( x^{5/2} \) as \( x^2 \cdot \sqrt{x} \):
\[ f(5x) = 25x^2\sqrt{5x} \]

### Final Answer:
Thus, the final expression for \( f(5x) \) is:
\[ f(5x) = 25x^2\sqrt{5x} \]