-3√16a + 5a√16ab²

It looks like you have a series of mathematical expressions involving square roots. Here's a breakdown of the steps to simplify these expressions where applicable:

1. **Expression**: \(-\frac{3\sqrt{16a} + 5a\sqrt{16ab^2}}{2\sqrt{a}} \quad (a > 0, b > 0)\)
- Simplify \(\sqrt{16a} = 4\sqrt{a}\)
- Simplify \(\sqrt{16ab^2} = 4b\sqrt{a}\), thus \(5a\sqrt{16ab^2} = 20ab\)
- The expression becomes:
\[
-\frac{3(4\sqrt{a}) + 20ab}{2\sqrt{a}} = -\frac{12\sqrt{a} + 20ab}{2\sqrt{a}} = -6 - 10b
\]

2. **Expression a)**: \(\sqrt{3} - \sqrt{2} + \sqrt{1 - \sqrt{2}}^2\)
- Calculate \((\sqrt{1 - \sqrt{2}})^2\)

3. **Expression b)**: \(\sqrt{(7 - 3)^2} + \sqrt{(7 + 3)^2}\)
- Simplifying gives \(\sqrt{(4)^2} + \sqrt{(10)^2} = 4 + 10 = 14\)

4. **Expression 3)**: \(\sqrt{192 - 75}\)
- Simplify: \(192 - 75 = 117\), thus \(\sqrt{117}\)

5. **Expression 4 b)**: \(-\frac{3}{18} + \frac{5\sqrt{50} - \sqrt{128}}{7\sqrt{2}}\)
- Simplify \(\sqrt{50} = 5\sqrt{2}\) and \(\sqrt{128} = 8\sqrt{2}\).

6. **Expressions with cubes**:
- For \(\sqrt{(1 - \sqrt{2})^3}\) and \(\sqrt{(2\sqrt{2} + 1)^3}\), calculate the cubes and then compute the square roots.
- Apply either binomial expansion or direct multiplication methods.

This allows you to simplify these expressions step by step. If you need further help on any specific part, feel free to ask!