Risoluzione espressione

(4 + 1/2)^(-2)/(1 - 1/9)^2 + (-2)^(-3) - ((- 2/3)^(-4)/(9/4)^(-2)·(- 2/3)^7 - 2^(-3)/5) - (- 2/5)^(-2)·5^(-1)=

=(9/2)^(-2)/(8/9)^2 - 1/8 - (81/16/(16/81)·(- 2/3)^7 - 1/40) - 25/4·(1/5)=

=1/16 - 1/8 - (81/16/(16/81)·(- 2/3)^7 - 1/40) - 25/4·(1/5)=

=1/16 - 1/8 - (3^8/2^8·(- 2/3)^7 - 1/40) - 5/4=

=1/16 - 1/8 - (- 3/2 - 1/40) - 5/4=

=1/16 - 1/8 + 61/40 - 5/4=

=(1·5 - 1·10 + 61·2 - 5·20)/80 = 17/80

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274)

$\small \left(4+\dfrac{1}{2}\right)^{-2}÷\left(1-\dfrac{1}{9}\right)^2+\left(-2\right)^{-3}-\left[\left(-\dfrac{2}{3}\right)^{-4}÷\left(\dfrac{9}{4}\right)^{-2}·\left(-\dfrac{2}{3}\right)^7-\dfrac{2^{-3}}{5}\right]-\left(-\dfrac{2}{5}\right)^{-2}·5^{-1}=$

$\small = \left(\dfrac{8+1}{2}\right)^{-2}÷\left(\dfrac{9-1}{9}\right)^2+\left(-\dfrac{1}{2}\right)^{3}-\left[\left(-\dfrac{3}{2}\right)^4÷\left(\dfrac{4}{9}\right)^2·\left(-\dfrac{2}{3}\right)^7-\dfrac{\left(\dfrac{1}{2}\right)^3}{5}\right]-\left(-\dfrac{5}{2}\right)^2·\dfrac{1}{5}=$

$\small = \left(\dfrac{9}{2}\right)^{-2}÷\left(\dfrac{8}{9}\right)^2-\dfrac{1}{8}-\left[\left(-\dfrac{3}{2}\right)^4·\left(\dfrac{9}{4}\right)^2·\left(-\dfrac{2}{3}\right)^7-\dfrac{\dfrac{1}{8}}{5}\right]-\dfrac{\cancel{25}^5}{4}·\dfrac{1}{\cancel5_1}=$

$\small = \left(\dfrac{\cancel2^1}{\cancel9_1}\right)^2·\left(\dfrac{\cancel9^1}{\cancel8_4}\right)^2-\dfrac{1}{8}-\left[\left(-\dfrac{3}{2}\right)^4·\left(\dfrac{3}{2}\right)^2·\left(\dfrac{3}{2}\right)^2·\left(-\dfrac{2}{3}\right)^7-\dfrac{1}{8}·\dfrac{1}{5}\right]-\dfrac{5}{4}·\dfrac{1}{1}=$

$\small = \left(\dfrac{1}{1}\right)^2·\left(\dfrac{1}{4}\right)^2-\dfrac{1}{8}-\left[\left(\dfrac{3}{2}\right)^{4+2+2}·\left(-\dfrac{2}{3}\right)^7-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = 1·\dfrac{1}{16}-\dfrac{1}{8}-\left[\left(\dfrac{3}{2}\right)^8·\left(-\dfrac{2}{3}\right)^7-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[\dfrac{3}{2}·\left(\dfrac{\cancel3^1}{\cancel2_1}\right)^7·\left(-\dfrac{\cancel2^1}{\cancel3_1}\right)^7-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[\dfrac{3}{2}·1^7·-1^7-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[\dfrac{3}{2}·1·-1-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[-\dfrac{3}{2}-\dfrac{1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[\dfrac{-60-1}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}-\left[-\dfrac{61}{40}\right]-\dfrac{5}{4}=$

$\small = \dfrac{1}{16}-\dfrac{1}{8}+\dfrac{61}{40}-\dfrac{5}{4}=$

$\small = \dfrac{5-10+122-100}{80} =$

$\small = \dfrac{17}{80} $