Вопрос:

Вычислите: 1) \(7\cdot\left(\frac{1}{7}\right)^2-8\cdot\frac{1}{7}\); 2) \(\frac{4.2}{8.2-7.4}\); 3) \(\frac{1.7+3.8}{2.2}\); 4) \(\frac{2.1\cdot3.5}{4.9}\); 5) \(2.5\cdot3.5-0.35\); 6) \((5\cdot10^{-2})^3\cdot(2\cdot10^3)\).

Ответ:

  1. \[7\cdot\left(\frac{1}{7}\right)^2-8\cdot\frac{1}{7}=\frac{1}{7}-\frac{8}{7}=-1\]
  2. \[\frac{4.2}{8.2-7.4}=\frac{4.2}{0.8}=5.25\]
  3. \[\frac{1.7+3.8}{2.2}=\frac{5.5}{2.2}=2.5\]
  4. \[\frac{2.1\cdot3.5}{4.9}=\frac{7.35}{4.9}=1.5\]
  5. \[2.5\cdot3.5-0.35=8.75-0.35=8.4\]
  6. \[(5\cdot10^{-2})^3\cdot(2\cdot10^3)=125\cdot10^{-6}\cdot2\cdot10^3=250\cdot10^{-3}=0.25\]

Ответ: −1; 5.25; 2.5; 1.5; 8.4; 0.25.