https://r2.erweima.ai/mathbot/image/1727013125894n9xczuft.jpg

The expression in the image appears to be:

\[
\frac{\left( x^{\frac{1}{5}} \right)^3}{\sqrt[5]{x^4}}
\]

### Let's simplify step-by-step:

1. **Simplify the numerator**:
   - The numerator is \( \left( x^{\frac{1}{5}} \right)^3 \). 
   - By the power rule \( (x^m)^n = x^{m \cdot n} \), this becomes:
     \[
     x^{\frac{1}{5} \cdot 3} = x^{\frac{3}{5}}
     \]

2. **Simplify the denominator**:
   - The denominator is \( \sqrt[5]{x^4} \), which is equivalent to \( x^{\frac{4}{5}} \).

3. **Combine the expression**:
   - Now the expression becomes:
     \[
     \frac{x^{\frac{3}{5}}}{x^{\frac{4}{5}}}
     \]
   - Using the rule \( \frac{x^m}{x^n} = x^{m - n} \), we subtract the exponents:
     \[
     x^{\frac{3}{5} - \frac{4}{5}} = x^{-\frac{1}{5}}
     \]

Thus, the simplified form of the expression is:

\[
x^{-\frac{1}{5}} = \frac{1}{x^{\frac{1}{5}}}
\]

### Final Answer:
\[
\frac{1}{x^{\frac{1}{5}}}
\]

---

Do you have any questions or would you like further explanation? 

Here are some related questions to explore:

1. What are the general rules for simplifying fractional exponents?
2. How can you express \( x^{-\frac{1}{5}} \) as a radical?
3. How do you simplify an expression involving a square root in the denominator?
4. What is the difference between positive and negative exponents in expressions?
5. How do the rules for dividing powers apply to expressions with different bases?

**Tip:** When dealing with fractional exponents, remember that \( x^{\frac{a}{b}} \) can be written as the \( b \)-th root of \( x^a \), which helps in converting between radical and exponential forms.

Simplify the expression ((x^(1/5))^3)/(√[5](x^4))

Learn how to simplify the expression ((x^(1/5))^3)/(√[5](x^4)) step by step using laws of exponents and radicals. Understand the conversion between radicals and exponents and the rules for dividing powers. Suitable for high school students in Grades 10-12.

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