3. Найдите значение выражения: a) $$b^{-19} \cdot (4b^7)^3$$ при $$b = -0.5$$ б) $$\frac{(a-2)^2 - 2(a-2) + 1}{a-3}$$ при $$a = 0.71$$ в) $$\frac{x^3y + xy^3}{2(y-x)} \cdot \frac{5(x-y)}{x^2 + y^2}$$ при $$x = -3$$ и $$y = \frac{1}{3}$$

a) $$b^{-19} \cdot (4b^7)^3 = b^{-19} \cdot 4^3 \cdot b^{21} = 64 \cdot b^{-19+21} = 64b^2$$ При $$b = -0.5$$: $$64 \cdot (-0.5)^2 = 64 \cdot 0.25 = 16$$ $$\bold{16}$$ б) $$\frac{(a-2)^2 - 2(a-2) + 1}{a-3} = \frac{((a-2) - 1)^2}{a-3} = \frac{(a-3)^2}{a-3} = a-3$$ При $$a = 0.71$$: $$0.71 - 3 = -2.29$$ $$\bold{-2.29}$$ в) $$\frac{x^3y + xy^3}{2(y-x)} \cdot \frac{5(x-y)}{x^2 + y^2} = \frac{xy(x^2 + y^2)}{2(y-x)} \cdot \frac{5(x-y)}{x^2 + y^2} = \frac{xy \cdot 5(x-y)}{2(y-x)} = \frac{5xy(x-y)}{-2(x-y)} = -\frac{5}{2}xy$$ При $$x = -3$$ и $$y = \frac{1}{3}$$: $$-\frac{5}{2} \cdot (-3) \cdot \frac{1}{3} = \frac{5}{2} \cdot 1 = \frac{5}{2} = 2.5$$ $$\bold{2.5}$$