It looks like you're asking to simplify the following expression:

\[
\sqrt{\frac{x^{2/3} + y^{2/3}}{x^{2/3}}}
\]

Let's break it down step by step:

1. The expression inside the square root is:

\[
\frac{x^{2/3} + y^{2/3}}{x^{2/3}}
\]

2. We can split the fraction into two terms:

\[
\frac{x^{2/3}}{x^{2/3}} + \frac{y^{2/3}}{x^{2/3}}
\]

3. Simplify the first part, \(\frac{x^{2/3}}{x^{2/3}} = 1\), so the expression becomes:

\[
1 + \frac{y^{2/3}}{x^{2/3}}
\]

4. \(\frac{y^{2/3}}{x^{2/3}}\) can be written as \(\left(\frac{y}{x}\right)^{2/3}\), which simplifies the expression to:

\[
1 + \left(\frac{y}{x}\right)^{2/3}
\]

5. Now, we take the square root of the entire expression:

\[
\sqrt{1 + \left(\frac{y}{x}\right)^{2/3}}
\]

This is the simplified form of the expression.

Would you like more details on this, or do you have any questions?

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Here are 5 related questions:
1. How do you simplify fractional exponents?
2. What is the process for splitting a fraction into simpler terms?
3. How does the square root interact with exponents in a mathematical expression?
4. How do you manipulate expressions with terms in the form \(a^{m/n}\)?
5. What are the rules for working with radicals and fractional exponents?

**Tip:** When simplifying fractions involving exponents, remember that dividing powers with the same base subtracts their exponents!

Learn how to simplify the expression sqrt((x^(2/3)+y^(2/3))/x^(2/3)) with a detailed step-by-step solution. This problem explores key algebraic concepts, including radicals, exponents, and the properties of exponents, making it suitable for students in Grades 9-11.

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