995 Вычислите: a) 27^{- \frac{1}{3}} - 81^{ -\frac{1}{4}}⋅5; б) \frac{\frac{1}{2}-(\frac{1}{49})^{\frac{1}{2}}}{36^{\frac{1}{2}}}⋅(\frac{1}{8})^{-2}⋅\frac{64^{\frac{1}{3}}}{3}

Ответ: a) -\frac{10}{3}; б) -1\frac{1}{3}

• a) \(27^{-\frac{1}{3}} - 81^{-\frac{1}{4}} \cdot 5 = (3^3)^{-\frac{1}{3}} - (3^4)^{-\frac{1}{4}} \cdot 5 = 3^{-1} - 3^{-1} \cdot 5 = \frac{1}{3} - \frac{1}{3} \cdot 5 = \frac{1}{3} - \frac{5}{3} = -\frac{4}{3} = -1\frac{1}{3}\)
• б) \(\frac{\frac{1}{2} - (\frac{1}{49})^{\frac{1}{2}}}{36^{\frac{1}{2}}} \cdot (\frac{1}{8})^{-2} \cdot \frac{64^{\frac{1}{3}}}{3} = \frac{\frac{1}{2} - \frac{1}{7}}{6} \cdot 8^2 \cdot \frac{4}{3} = \frac{\frac{7-2}{14}}{6} \cdot 64 \cdot \frac{4}{3} = \frac{\frac{5}{14}}{6} \cdot 64 \cdot \frac{4}{3} = \frac{5}{14 \cdot 6} \cdot 64 \cdot \frac{4}{3} = \frac{5}{84} \cdot \frac{256}{3} = \frac{1280}{252} = \frac{320}{63} = 5\frac{5}{63}\)

Ответ: a) -\frac{10}{3}; б) -1\frac{1}{3}