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The task asks to convert a root expression into an exponential form. Specifically, the expression is \(\sqrt[7]{x^2}\).

To express \(\sqrt[7]{x^2}\) in exponential form, we use the property of exponents which states that the \(n\)-th root of a number can be written as a power of that number. In general:

\[
\sqrt[n]{a^m} = a^{m/n}
\]

Applying this to \(\sqrt[7]{x^2}\):

\[
\sqrt[7]{x^2} = x^{2/7}
\]

So, \(\sqrt[7]{x^2}\) in exponential form is \(x^{2/7}\).

Would you like any more details or have any questions about this process? Here are 5 related questions that expand on this topic:

1. How do you convert \(\sqrt[3]{x^5}\) into exponential form?
2. What is the general rule for converting a root expression into an exponential expression?
3. Can you express \(\sqrt[4]{y^3}\) in terms of a fractional exponent?
4. How do you handle converting a root expression with a coefficient, such as \(3\sqrt[5]{x^4}\), into exponential form?
5. What is the exponential form of \(\sqrt{a}\)?

**Tip:** Remember that \( \sqrt[n]{a^m} \) is equivalent to \( a^{m/n} \), where \(n\) is the root and \(m\) is the exponent inside the radical.

Esitä potenssilausekkeen muodossa \(\sqrt[7]{x^2}\)

Learn how to convert the root expression \(\sqrt[7]{x^2}\) into exponential form using exponentiation properties. This problem demonstrates the general rule for roots and powers, suitable for students in Grades 9-12.

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