Espressione numero 719 con risultato -8

Espressione n. 719

{[(5/4-3)^2-(1-5/2)^2-1/4:4]^3*(-32/9)}^3:[-(1/2-5/4)^3] =

719)

$\big\{\big[\big(\frac{5}{4}-3\big)^2-\big(1-\frac{5}{2}\big)^2-\frac{1}{4}÷4]^3·\big(-\frac{32}{9}\big)\big\}^3÷\big[-\big(\frac{1}{2}-\frac{5}{4}\big)^3\big]=$

$=\big\{\big[\big(\frac{5-12}{4}\big)^2-\big(\frac{2-5}{2}\big)^2-\frac{1}{4}·\frac{1}{4}]^3·\big(-\frac{32}{9}\big)\big\}^3÷\big[-\big(\frac{2-5}{4}\big)^3\big]=$

$=\big\{\big[\big(-\frac{7}{4}\big)^2-\big(-\frac{3}{2}\big)^2-\frac{1}{16}]^3·\big(-\frac{32}{9}\big)\big\}^3÷\big[-\big(-\frac{3}{4}\big)^3\big]=$

$=\big\{\big[\frac{49}{16}-\frac{9}{4}-\frac{1}{16}]^3·\big(-\frac{32}{9}\big)\big\}^3÷\big[-\big(-\frac{27}{64}\big)\big]=$

$=\big\{\big[\frac{49-36-1}{16}]^3·\big(-\frac{32}{9}\big)\big\}^3÷\frac{27}{64}=$

$=\big\{\big[\frac{12}{16}]^3·\big(-\frac{32}{9}\big)\big\}^3·\frac{64}{24}=$

$=\big\{\big[\frac{3}{4}]^3·\big(-\frac{32}{9}\big)\big\}^3·\frac{64}{27}=$

$=\big\{\frac{27}{64}·\big(-\frac{32}{9}\big)\big\}^3·\frac{64}{27}=$

$=\big\{\frac{3}{2}·\big(-\frac{1}{1}\big)\big\}^3·\frac{64}{27}=$

$=\big\{-\frac{3}{2}\big\}^3·\frac{64}{27}=$

$= \big(-\frac{27}{8}\big)·\frac{64}{27}=$

$= \big(-\frac{1}{1}\big)·\frac{8}{1}=$

$= -8$