https://file.aiquickdraw.com/mathbot/file/1726162176426z1k8xci9.jpg

The expression in the image is:

\[
\left(1 + 2\sqrt{3} - \sqrt{5}\right)^{\frac{3}{2}}
\]

Would you like me to simplify or evaluate this expression, or provide a step-by-step explanation for further understanding? Let me know how you'd like to proceed!

Here are a few related questions for deeper exploration:
1. How do you simplify expressions with square roots?
2. What does raising a binomial to a fractional power signify?
3. Can this expression be expressed in a simpler radical form?
4. How would the solution change if the power were different, such as \(\frac{5}{2}\)?
5. What is the role of the distributive property when working with nested radicals?

**Tip**: Remember that fractional exponents like \(\frac{3}{2}\) represent both a power and a root. The denominator indicates the root, and the numerator indicates the power.

Explore how to simplify and evaluate the expression (1 + 2√3 - √5)^(3/2), covering concepts like radical expressions, fractional exponents, and the binomial theorem. This problem is suited for students in Grades 10-12 and provides an in-depth explanation of exponents and radical terms.

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