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To express \((7x^3y^2)^{\frac{2}{7}}\) in radical form, let’s break it down.

1. **Rewrite the expression**: The exponent \(\frac{2}{7}\) indicates both a power and a root, meaning we raise \((7x^3y^2)\) to the power of 2, and then take the 7th root of the result.

   \[
   (7x^3y^2)^{\frac{2}{7}} = \sqrt[7]{(7x^3y^2)^2}
   \]

2. **Expand \((7x^3y^2)^2\)**: 
   - \(7^2 = 49\)
   - \((x^3)^2 = x^6\)
   - \((y^2)^2 = y^4\)
   
   So,
   \[
   (7x^3y^2)^2 = 49x^6y^4
   \]

3. **Combine in radical form**:
   \[
   (7x^3y^2)^{\frac{2}{7}} = \sqrt[7]{49x^6y^4}
   \]

The correct answer is:
- **Option B:** \(\sqrt[7]{49x^6y^4}\)

Would you like a further breakdown or have questions about any steps?

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Here are 5 related questions to deepen understanding:

1. How would you convert an expression with a fractional exponent like \(\frac{3}{4}\) to radical form?
2. If the expression had an exponent of \(\frac{1}{3}\) instead, what would the radical form look like?
3. How do you handle cases where the base contains multiple variables, like \((5a^2b^3)^{\frac{1}{5}}\)?
4. What if we had a negative exponent, such as \((x^2y^3)^{-\frac{1}{2}}\)?
5. How do you simplify \((2x^4y^2)^{\frac{3}{5}}\) in radical form?

**Tip:** Remember, the numerator of a fractional exponent indicates the power, and the denominator represents the root.

What is the expression in radical form? \((7x^3y^2)^{\frac{2}{7}}\)

Learn how to express (7x^3y^2)^(2/7) in radical form. This solution covers the laws of exponents and explains how to convert fractional exponents to radical notation. Suitable for students in Grades 10-12.

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