найти значение выражения

Давайте решим каждое выражение по очереди.

1. а) \(\left( \frac{8}{4} \right)^2 \cdot \frac{1}{3} \div (-0.5)^2 \):

   \(\frac{8}{4} = 2\)

   \(2^2 = 4\)

   \((-0.5)^2 = 0.25\)

   \(\frac{1}{3} \div 0.25 = \frac{1}{3} \times 4 = \frac{4}{3}\)

   \(4 \cdot \frac{4}{3} = \frac{16}{3}\)

2. б) \(3000 \cdot (0.2)^3 \div (-2)^6\):

   \(0.2^3 = 0.008\)

   \((-2)^6 = 64\)

   \(3000 \cdot 0.008 = 24\)

   \(\frac{24}{64} = \frac{3}{8}\)

3. а) \(\frac{1.6}{(0.4)^2} \cdot (-3)^3\):

   \(0.4^2 = 0.16\)

   \(\frac{1.6}{0.16} = 10\)

   \((-3)^3 = -27\)

   \(10 \cdot (-27) = -270\)

4. б) \(3^5 \cdot \left(-\frac{2}{3}\right)^3 + \frac{1}{(-0.1)^3}\):

   \(3^5 = 243\)

   \(\left(-\frac{2}{3}\right)^3 = -\frac{8}{27}\)

   \(243 \cdot -\frac{8}{27} = -72\)

   \((-0.1)^3 = -0.001\)

   \(\frac{1}{-0.001} = -1000\)

   \(-72 + (-1000) = -1072\)

Ответы:

1. а) \(-\frac{16}{3}\) б) \(\frac{3}{8}\)
2. а) \(-270\) б) \(-1072\)