To simplify \((x^6)^{\frac{5}{4}}\), we apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\).

So:

\[
(x^6)^{\frac{5}{4}} = x^{6 \cdot \frac{5}{4}} = x^{\frac{30}{4}} = x^{7.5}
\]

Thus, the simplified expression is:

\[
x^{7.5}
\]

Let me know if you'd like more details on this! Here are some related questions:

1. How would you simplify \((x^3)^{\frac{2}{3}}\)?
2. What is \((x^4)^{\frac{1}{2}}\)?
3. How would you approach \((x^{10})^{\frac{3}{5}}\)?
4. Can you simplify \((x^2)^{\frac{7}{3}}\)?
5. What happens when simplifying \((x^8)^{\frac{5}{6}}\)?

**Tip:** When simplifying powers, always multiply the exponents together.

Discover how to simplify the expression (x^6)^(5/4) step by step by applying the power of a power rule, (a^m)^n = a^(m * n). This solution covers key algebraic concepts, exponentiation rules, and is suitable for students in Grades 9-12.

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