Tính

To solve the expressions in the image, let's tackle each part step by step:

### a)
\[
\left( \frac{-5}{3} + \frac{1}{4} \right) \cdot \left( \frac{12}{5} - \frac{1}{2} \right)
\]

1. Find a common denominator:
- For \(-\frac{5}{3} + \frac{1}{4}\): common denominator is 12.
- \(-\frac{5}{3} = -\frac{20}{12}\) and \(\frac{1}{4} = \frac{3}{12}\).
- So, \(-\frac{20}{12} + \frac{3}{12} = -\frac{17}{12}\).

2. For \(\frac{12}{5} - \frac{1}{2}\):
- Common denominator is 10.
- \(\frac{12}{5} = \frac{24}{10}\) and \(-\frac{1}{2} = -\frac{5}{10}\).
- So, \(\frac{24}{10} - \frac{5}{10} = \frac{19}{10}\).

3. Now multiply:
\[
-\frac{17}{12} \cdot \frac{19}{10} = -\frac{323}{120}
\]

### b)
\[
-\frac{1}{15} + \frac{9}{21} + \left(-\frac{14}{15}\right) + \frac{12}{21} + 2
\]

1. Convert to common denominators:
- For \(-\frac{1}{15} - \frac{14}{15}\): result is \(-\frac{15}{15} = -1\).
- Combine:
- \(\frac{9}{21} + \frac{12}{21} = \frac{21}{21} = 1\).
- So, \(-1 + 1 + 2 = 2\).

### c)
\[
0.125 \cdot \left(-\frac{8}{35}\right)
\]

1. Convert \(0.125\) to a fraction:
\[
0.125 = \frac{1}{8}
\]
2. Multiply:
\[
\frac{1}{8} \cdot -\frac{8}{35} = -\frac{1}{35}
\]

### d)
\[
0.2 \cdot \left(-\frac{3}{8} \cdot \frac{1}{5} \cdot \left(-\frac{5}{8}\right)\right)
\]

1. Calculate \(-\frac{3}{8} \cdot \frac{1}{5} \cdot \left(-\frac{5}{8}\right)\):
- Negative signs cancel.
- Result is \(\frac{3 \cdot 5}{8 \cdot 5 \cdot 8} = \frac{15}{320} = \frac{3}{64}\).

2. Multiply by \(0.2\):
\[
0.2 \cdot \frac{3}{64} = \frac{2}{10} \cdot \frac{3}{64} = \frac{6}{640} = \frac{3}{320}
\]

### e)
\[
\sqrt{(-3)^2} \cdot \frac{2}{3} \cdot \sqrt{8^2} \cdot 0.5
\]

1. Calculate:
\(\sqrt{(-3)^2} = 3\), \(\sqrt{8^2} = 8\).

2. Multiply:
\[
3 \cdot \frac{2}{3} \cdot 8 \cdot 0.5 = 2 \cdot 8 \cdot 0.5 = 8
\]

### f)
\[
-\left(-\frac{3}{2}\right) \cdot \frac{13}{7}
\]

1. Multiply:
\[
\frac{3}{2} \cdot \frac{13}{7} = \frac{39}{14}
\]

In conclusion, the results are:

### Answers
- a) \(-\frac{323}{120}\)
- b) \(2\)
- c) \(-\frac{1}{35}\)
- d) \(\frac{3}{320}\)
- e) \(8\)
- f) \(\frac{39}{14}\)