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The given question is asking for an expression equivalent to \( t^{\frac{2}{7}} \).

Let's solve it by converting the expression to a radical form. Here's how the conversion works:

1. The expression \( t^{\frac{2}{7}} \) means:
   - The denominator (7) represents the root.
   - The numerator (2) represents the exponent (or power).

Thus, \( t^{\frac{2}{7}} \) can be rewritten as:

\[
\left( \sqrt[7]{t} \right)^2
\]

This corresponds to taking the 7th root of \( t \) and then squaring it.

Now, comparing this result with the provided options:

1. \( t^6 \) – This is not equivalent because the exponent is 6, not \( \frac{2}{7} \).
2. \( \sqrt[7]{t} \) – This only represents \( t^{\frac{1}{7}} \), missing the square (power of 2).
3. \( \left( \sqrt[7]{t} \right)^2 \) – This matches our answer.
4. \( \frac{\sqrt{t}}{t} \) – This represents something else entirely and is not equivalent.

Therefore, the correct option is **\( \left( \sqrt[7]{t} \right)^2 \)**.

Would you like more details or explanations on this topic?

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Here are five related questions to consider:
1. How would you convert \( t^{\frac{5}{3}} \) into a radical expression?
2. What is the difference between \( t^{\frac{1}{n}} \) and \( t^n \)?
3. How do you simplify \( \sqrt[3]{x^6} \)?
4. What happens when you multiply two expressions with rational exponents, like \( t^{\frac{1}{3}} \times t^{\frac{1}{2}} \)?
5. How do you convert radical expressions back to rational exponents?

**Tip:** Always remember that the numerator of a rational exponent is the power, and the denominator is the root when converting between exponent and radical forms.

Which expression is equivalent to t^(2/7)?

Learn how to convert t^(2/7) to an equivalent radical expression. This involves breaking down rational exponents where the denominator represents the root and the numerator represents the power. Ideal for students in grades 8-10 studying exponents and radicals.

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