It seems that you are working with an expression involving square roots and exponents. I assume your expression is:

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

Let's simplify this step by step.

1. First, split the terms in the numerator:
\[
\sqrt{\frac{x^{2/3}}{x^{2/3}} + \frac{y^{2/3}}{x^{2/3}}}
\]

2. Simplify \(\frac{x^{2/3}}{x^{2/3}} = 1\), so the expression becomes:
\[
\sqrt{1 + \frac{y^{2/3}}{x^{2/3}}}
\]

3. Recall that \(\frac{y^{2/3}}{x^{2/3}} = \left(\frac{y}{x}\right)^{2/3}\), so the expression simplifies to:
\[
\sqrt{1 + \left(\frac{y}{x}\right)^{2/3}}
\]

Thus, the simplified form of the expression is:

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

Let me know if you want further explanation or additional details.

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Here are five related questions you might want to consider:
1. How do you simplify radicals involving fractional exponents?
2. What are the properties of exponents that help simplify expressions like these?
3. How would this expression change if the powers of \(x\) and \(y\) were different?
4. Can you graph the function \(\sqrt{1 + \left(\frac{y}{x}\right)^{2/3}}\)?
5. How does the behavior of the function change as \(x \to 0\)?

**Tip:** When dealing with expressions involving exponents and radicals, always try to rewrite them in a simpler form using properties of exponents for easier manipulation.

Explore the step-by-step simplification of the expression sqrt((x^(2/3) + y^(2/3))/x^(2/3)). Learn about key algebraic concepts including exponent rules, properties of radicals, and simplification techniques. Ideal for students in Grades 9-12.

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