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To express \( 2^{\frac{3}{5}} \) in the form of a root, we can use the relationship between exponents and radicals. The expression \( a^{\frac{m}{n}} \) can be rewritten as the \( n \)-th root of \( a^m \), which is \( \sqrt[n]{a^m} \).

For \( 2^{\frac{3}{5}} \):

1. Identify \( a = 2 \), \( m = 3 \), and \( n = 5 \).
2. Rewrite \( 2^{\frac{3}{5}} \) as the 5th root of \( 2^3 \):

\[
2^{\frac{3}{5}} = \sqrt[5]{2^3}
\]

So, \( 2^{\frac{3}{5}} \) in the form of a root is \( \sqrt[5]{2^3} \).

Would you like more details or have any questions?

Here are some related questions for further practice:
1. How would you express \( 3^{\frac{4}{7}} \) in the form of a root?
2. What is \( 5^{\frac{2}{3}} \) in the form of a root?
3. Can you write \( 10^{\frac{1}{4}} \) as a radical?
4. How would you express \( 7^{\frac{5}{6}} \) using a root?
5. Rewrite \( 9^{\frac{2}{5}} \) in radical form.

**Tip:** Remember that \( a^{\frac{m}{n}} \) can always be expressed as the \( n \)-th root of \( a^m \). This is a useful way to transform exponent expressions into root form.

Learn how to express 2^(3/5) in the form of a root using the relationship between exponents and radicals. This example uses the formula a^(m/n) = sqrt[n]{a^m}. Suitable for students in Grades 9-11.

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