https://r2.erweima.ai/mathbot/image/17272005622578xkerzyi.jpg

It appears there was an issue loading the Spanish language data for text extraction. However, based on the image, I can manually interpret the expression:

The given expression is:

\[
5 \sqrt[3]{3} - \frac{2}{5} \sqrt[3]{3} + \frac{1}{4} \sqrt[6]{32}
\]

Let’s simplify this step by step:

### Step 1: Simplify the terms involving \( \sqrt[3]{3} \)

First, combine like terms involving \( \sqrt[3]{3} \):

\[
5 \sqrt[3]{3} - \frac{2}{5} \sqrt[3]{3} = \left(5 - \frac{2}{5}\right) \sqrt[3]{3}
\]

Simplify the coefficient:

\[
5 - \frac{2}{5} = \frac{25}{5} - \frac{2}{5} = \frac{23}{5}
\]

Thus, we have:

\[
\frac{23}{5} \sqrt[3]{3}
\]

### Step 2: Simplify \( \frac{1}{4} \sqrt[6]{32} \)

We can express \( \sqrt[6]{32} \) as \( \sqrt[6]{2^5} \), which simplifies to \( 2^{5/6} \).

Thus:

\[
\frac{1}{4} \cdot 2^{5/6}
\]

### Final Expression:

Now, combining the results, the simplified form is:

\[
\frac{23}{5} \sqrt[3]{3} + \frac{1}{4} \cdot 2^{5/6}
\]

Would you like to dive deeper into any part of this simplification?

Here are 5 questions related to this:

1. How do you simplify cube roots or sixth roots in algebraic expressions?
2. What is the general process for combining like terms with roots?
3. How does one convert a radical expression like \( \sqrt[6]{32} \) to exponential form?
4. What are the differences between fractional exponents and radical expressions?
5. How can you further approximate the expression \( 2^{5/6} \)?

**Tip:** Always check if the terms have a common radical before simplifying!

Calcula lo más simplificado posible: 5√³3 − (2/5)√³3 + (1/4)√⁶(3²)

Learn how to simplify the radical expression 5√³3 − (2/5)√³3 + (1/4)√⁶(3²) with step-by-step guidance. This algebraic problem involves cube roots, sixth roots, and combining like terms. Suitable for students in Grades 10-12.

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