Rešite (1/3+frac{7/9)^{2}}{(1-1/2)^2*(-2)^3-3/2}+[-(-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}}=

$$\frac { ( \frac { 1 } { 3 } + \frac { 7 } { 9 } ) ^ { 2 } } { ( 1 - \frac { 1 } { 2 } ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } - \frac { 3 } { 2 } } + [ - ( - \frac { 1 } { 6 } ) ^ { 2 } + \frac { \frac { 1 } { 4 } - \frac { 1 } { 5 } } { ( 1 - \frac { 2 } { 5 } ) ^ { 2 } } ] - \frac { \frac { 1 } { 3 } - \frac { 2 } { 9 } } { \frac { 1 } { 8 } - \frac { 15 } { 8 } } =$$

Ovrednoti

$$-\frac{101}{567}\approx -0,178130511$$

Koraki rešitve

Seštejte \frac{1}{3} in \frac{7}{9}, da dobite \frac{10}{9}.

$$\frac{\left(\frac{10}{9}\right)^{2}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Izračunajte potenco \frac{10}{9} števila 2, da dobite \frac{100}{81}.

$$\frac{\frac{100}{81}}{\left(1-\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$\frac{\frac{100}{81}}{\left(\frac{1}{2}\right)^{2}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$\frac{\frac{100}{81}}{\frac{1}{4}\left(-2\right)^{3}-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$\frac{\frac{100}{81}}{\frac{1}{4}\left(-8\right)-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$\frac{\frac{100}{81}}{-2-\frac{3}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$\frac{\frac{100}{81}}{-\frac{7}{2}}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Delite \frac{100}{81} s/z -\frac{7}{2} tako, da pomnožite \frac{100}{81} z obratno vrednostjo -\frac{7}{2}.

$$\frac{100}{81}\left(-\frac{2}{7}\right)-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Pomnožite \frac{100}{81} in -\frac{2}{7}, da dobite -\frac{200}{567}.

$$-\frac{200}{567}-\left(-\frac{1}{6}\right)^{2}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{200}{567}-\frac{1}{36}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Odštejte \frac{1}{36} od -\frac{200}{567}, da dobite -\frac{863}{2268}.

$$-\frac{863}{2268}+\frac{\frac{1}{4}-\frac{1}{5}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{863}{2268}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{863}{2268}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{863}{2268}+\frac{\frac{1}{20}}{\frac{9}{25}}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{863}{2268}+\frac{1}{20}\times \frac{25}{9}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{863}{2268}+\frac{5}{36}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Seštejte -\frac{863}{2268} in \frac{5}{36}, da dobite -\frac{137}{567}.

$$-\frac{137}{567}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{137}{567}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{137}{567}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

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

$$-\frac{137}{567}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

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

$$-\frac{137}{567}-\left(-\frac{4}{63}\right)$$

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

$$-\frac{137}{567}+\frac{4}{63}$$

Seštejte -\frac{137}{567} in \frac{4}{63}, da dobite -\frac{101}{567}.

$$-\frac{101}{567}$$

Faktoriziraj

$$-\frac{101}{567} = -0,1781305114638448$$