• 15.25 Вычислите: a) (1/2)² + (2/√3)^-4 ⋅ (3)-2; б) (√2/3)^-2 - (3/√2)^-4 : (3)¯³;

15.25 Вычислите:

а) $$ (\frac{1}{2})^2 + (\frac{2}{\sqrt{3}})^{-4} \cdot (3)^{-2} = \frac{1}{4} + (\frac{\sqrt{3}}{2})^4 \cdot \frac{1}{3^2} = \frac{1}{4} + \frac{(\sqrt{3})^4}{2^4} \cdot \frac{1}{9} = \frac{1}{4} + \frac{9}{16} \cdot \frac{1}{9} = \frac{1}{4} + \frac{1}{16} = \frac{4}{16} + \frac{1}{16} = \frac{5}{16} $$.

б) $$ (\frac{\sqrt{2}}{3})^{-2} - (\frac{3}{\sqrt{2}})^{-4} : (3)^{-3} = (\frac{3}{\sqrt{2}})^{2} - (\frac{\sqrt{2}}{3})^{4} : (\frac{1}{3})^3 = \frac{9}{2} - \frac{4}{81} : \frac{1}{27} = \frac{9}{2} - \frac{4}{81} \cdot 27 = \frac{9}{2} - \frac{4}{3} = \frac{27}{6} - \frac{8}{6} = \frac{19}{6} $$.

Ответ: а) 5/16; б) 19/6