1. Вычислите: a) (\(-\frac{1}{3}\))^{-3} \(\cdot\) (-3)^0 : \(\frac{2^{-3} \cdot 4^2}{8^{-2}}\) б) \(\sqrt{\frac{\sqrt{3}}{2}}\)^{-2} \(\cdot\) (1,5)^{-3} a) (-2)^0 \(\cdot\) \(-\frac{1}{2}\)^{-2} : \(\frac{3^{-3} \cdot 9^{-3}}{27^{-2}}\) б) (2,5)^{-3} \(\cdot\) \(\sqrt{\frac{\sqrt{5}}{2}}\)^{-2}

1. Вычисление выражений:

1. а) \(\(-\frac{1}{3}\))^{-3} \(\cdot\) (-3)^0 : \(\frac{2^{-3} \cdot 4^2}{8^{-2}}\) = (-3)^3 \(\cdot\) 1 : \(\frac{\frac{1}{8} \cdot 16}{1728}\) = -27 : \(\frac{2}{1728}\) = -27 \(\cdot\) \(\frac{1728}{2}\) = -27 \(\cdot\) 864 = -23328\)
2. б) \(\sqrt{\frac{\sqrt{3}}{2}}^{-2} \cdot (1,5)^{-3} = \left(\left(\frac{\sqrt{3}}{2}\right)^{\frac{1}{2}}\right)^{-2} \cdot \left(\frac{3}{2}\right)^{-3} = \left(\frac{\sqrt{3}}{2}\right)^{-1} \cdot \left(\frac{2}{3}\right)^3 = \frac{2}{\sqrt{3}} \cdot \frac{8}{27} = \frac{16}{27\sqrt{3}} = \frac{16\sqrt{3}}{81}\)
3. а) \( (-2)^0 \cdot (-\frac{1}{2})^{-2} : \frac{3^{-3} \cdot 9^{-3}}{27^{-2}} = 1 \cdot (-2)^2 : \frac{\frac{1}{27} \cdot \frac{1}{729}}{\frac{1}{729}} = 4 : \frac{1}{27} = 4 \cdot 27 = 108\)
4. б) \( (2,5)^{-3} \cdot \sqrt{\frac{\sqrt{5}}{2}}^{-2} = (\frac{5}{2})^{-3} \cdot (\frac{\sqrt{5}}{2})^{-\frac{1}{2} \cdot 2} = (\frac{2}{5})^3 \cdot (\frac{\sqrt{5}}{2})^{-1} = \frac{8}{125} \cdot \frac{2}{\sqrt{5}} = \frac{16}{125\sqrt{5}} = \frac{16\sqrt{5}}{625}\)

Ответ: а) -23328; б) \(\frac{16\sqrt{3}}{81}\); а) 108; б) \(\frac{16\sqrt{5}}{625}\).