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To simplify the given expression \(\displaystyle x^{\frac{6}{7}}\), we can rewrite it in radical form. The expression \(\displaystyle x^{\frac{6}{7}}\) can be expressed as:

\[
x^{\frac{6}{7}} = \left(\sqrt[7]{x}\right)^6
\]

Alternatively, it can be written as:

\[
x^{\frac{6}{7}} = \sqrt[7]{x^6}
\]

In the provided problem, the format seems to require the use of a radical with a specific index. Therefore, the simplified form of \(\displaystyle x^{\frac{6}{7}}\) is:

\[
x^{\frac{6}{7}} = \sqrt[7]{x^6}
\]

Would you like more details or have any questions?

Here are some related questions you might explore:
1. How do you simplify expressions with fractional exponents?
2. What is the difference between \(\sqrt[n]{x^m}\) and \(\left(\sqrt[n]{x}\right)^m\)?
3. How do you convert a radical expression back into an exponent form?
4. What are some examples of simplifying expressions with different fractional exponents?
5. How can you simplify \(\displaystyle x^{\frac{3}{4}}\)?

**Tip:** When simplifying expressions with fractional exponents, remember that the denominator of the exponent represents the root, and the numerator represents the power.

Simplify the expression x^(6/7) and express it in radical form.

Learn how to simplify the expression x^(6/7) by converting it into radical form. Understand the key concepts of exponents and radicals, and follow the step-by-step solution. Suitable for students in Grades 9-11.

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