The solution to the expression $393 - \left(25 \times 6 - \left( \sqrt{22^2 + 32} + 36^{\frac{3}{5}} \right) \right)$ is approximately $274.30$.

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Here are 5 related questions you might find helpful:

1. How is the square root function applied in similar expressions?
2. How do fractional exponents like $36^{3/5}$ work?
3. Can this expression be solved step by step manually?
4. What are common mistakes when simplifying nested expressions?
5. How do calculators handle operations with square roots and exponents?

Tip: When working with complex expressions, it's helpful to simplify inner parentheses and roots first before applying other operations.