Rešite (1-1/2)^2(-2)^3-3/2+-(-1/6)^2+frac{1/4-frac{1}{5}}{(1-frac{2}{5})^2}|-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}

$$( 1 - \frac { 1 } { 2 } ) ^ { 2 } ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } + - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } | - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } }$$

Ovrednoti

$$-\frac{7981}{2268}\approx -3,518959436$$

Koraki rešitve

Odštejte \frac{1}{2} od 1, da dobite \frac{1}{2}.

$$\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Izračunajte potenco \frac{1}{2} števila 2, da dobite \frac{1}{4}.

$$\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Izračunajte potenco -2 števila 3, da dobite -8.

$$\frac{1}{4}\left(-8\right)-\frac{3}{2}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Pomnožite \frac{1}{4} in -8, da dobite -2.

$$-2-\frac{3}{2}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{3}{2} od -2, da dobite -\frac{7}{2}.

$$-\frac{7}{2}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Izračunajte potenco -\frac{1}{6} števila 2, da dobite \frac{1}{36}.

$$-\frac{7}{2}-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{1}{36} od -\frac{7}{2}, da dobite -\frac{127}{36}.

$$-\frac{127}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{1}{5} od \frac{1}{4}, da dobite \frac{1}{20}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{2}{5} od 1, da dobite \frac{3}{5}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Izračunajte potenco \frac{3}{5} števila 2, da dobite \frac{9}{25}.

$$-\frac{127}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Delite \frac{1}{20} s/z \frac{9}{25} tako, da pomnožite \frac{1}{20} z obratno vrednostjo \frac{9}{25}.

$$-\frac{127}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Pomnožite \frac{1}{20} in \frac{25}{9}, da dobite \frac{5}{36}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{2}{9} od \frac{1}{3}, da dobite \frac{1}{9}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}|$$

Odštejte \frac{15}{8} od \frac{1}{8}, da dobite -\frac{7}{4}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{\frac{1}{9}}{-\frac{7}{4}}|$$

Delite \frac{1}{9} s/z -\frac{7}{4} tako, da pomnožite \frac{1}{9} z obratno vrednostjo -\frac{7}{4}.

$$-\frac{127}{36}+\frac{5}{36}|-\frac{1}{9}\left(-\frac{4}{7}\right)|$$

Pomnožite \frac{1}{9} in -\frac{4}{7}, da dobite -\frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}|-\left(-\frac{4}{63}\right)|$$

Nasprotna vrednost -\frac{4}{63} je \frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}|\frac{4}{63}|$$

Absolutna vrednost realnega števila a je a, ko je a\geq 0, ali -a, ko je a<0. Absolutna vrednost števila \frac{4}{63} je \frac{4}{63}.

$$-\frac{127}{36}+\frac{5}{36}\times \frac{4}{63}$$

Pomnožite \frac{5}{36} in \frac{4}{63}, da dobite \frac{5}{567}.

$$-\frac{127}{36}+\frac{5}{567}$$

Seštejte -\frac{127}{36} in \frac{5}{567}, da dobite -\frac{7981}{2268}.

$$-\frac{7981}{2268}$$

Faktoriziraj

$$-\frac{7981}{2268} = -3\frac{1177}{2268} = -3,5189594356261025$$