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To rewrite the given expression \(\left(\sqrt[6]{9q}\right)^2\) in exponential form, we can break it down step by step.

1. **Expression:** \(\left(\sqrt[6]{9q}\right)^2\)

   The radical (root) expression \(\sqrt[6]{9q}\) means the 6th root of \(9q\). In exponential form, the 6th root of a number can be written as raising the number to the power of \( \frac{1}{6} \).

   Therefore, \(\sqrt[6]{9q}\) becomes \((9q)^{\frac{1}{6}}\).

2. **Square the expression:**

   Now, squaring this entire expression, we raise it to the power of 2:

   \[
   \left( (9q)^{\frac{1}{6}} \right)^2 = (9q)^{\frac{2}{6}} = (9q)^{\frac{1}{3}}
   \]

Thus, the exponential form of the given expression is:

\[
(9q)^{\frac{1}{3}}
\]

Would you like further details on this process, or do you have any other questions?

### Here are some related questions:
1. How do you convert higher-order roots (like cube or 5th roots) into exponential form?
2. Can you apply this method to expressions with variables raised to powers as well?
3. How would you handle a cube root of a fraction in exponential form?
4. What happens when you take the root of an expression with a negative exponent?
5. How do you simplify expressions involving both radicals and exponents?

**Tip:** Always remember, \(n\)-th roots can be written as fractional exponents, where the denominator of the fraction represents the root.

Write the expression (6th root of (9q))^2 in exponential form.

Learn how to convert the 6th root of (9q)^2 into exponential form with a detailed step-by-step explanation. This problem covers key concepts in algebra related to radicals and exponents. Suitable for students in Grades 9-10.

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