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.