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The equation shown is:

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

### Step-by-step solution:

1. **Simplify the numerator:**
   \[
   \left(x^{\frac{1}{3}}\right)^5 = x^{\frac{5}{3}}
   \]
   Using the power of a power rule: \((x^m)^n = x^{m \cdot n}\).

2. **Simplify the denominator:**
   \[
   \sqrt[4]{x^5} = x^{\frac{5}{4}}
   \]
   Using the rule: \(\sqrt[n]{x^m} = x^{\frac{m}{n}}\).

3. **Write the entire expression:**
   \[
   \frac{x^{\frac{5}{3}}}{x^{\frac{5}{4}}}
   \]
   When dividing powers with the same base, subtract the exponents: \(\frac{x^m}{x^n} = x^{m - n}\).

4. **Subtract the exponents:**
   \[
   \frac{5}{3} - \frac{5}{4} = \frac{20}{12} - \frac{15}{12} = \frac{5}{12}
   \]
   So the expression simplifies to:
   \[
   x^{\frac{5}{12}}
   \]

5. **Equate this to \(x^a\):**
   \[
   x^{\frac{5}{12}} = x^a
   \]

6. **Conclusion:**
   Since the bases are the same, the exponents must be equal:
   \[
   a = \frac{5}{12}
   \]

Thus, \(a = \frac{5}{12}\).

---

Would you like more details or have any questions about this? 

Here are some related questions for practice:
1. How do you apply the exponent rules in multiplication and division of powers?
2. Can you simplify \(\sqrt[3]{x^6}\) using fractional exponents?
3. What happens if the base of the powers in the equation are different?
4. How would the solution change if the numerator had a different exponent?
5. What is the general form for converting radical expressions to exponents?

**Tip:** When solving equations with exponents, always use exponent rules like multiplication, division, and powers of powers to simplify expressions.

Solve for a in the equation: (x^(1/3))^5 / (x^5)^(1/4) = x^a

Solve the algebraic equation (x^(1/3))^5 / (x^5)^(1/4) = x^a step-by-step, using exponent rules and simplifying fractional exponents. This problem is ideal for high school students (Grades 9-12) learning about exponents and algebra.

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