Riješi -(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}]^2-frac{frac{1}{3}-frac{2}{9}}{frac{1}{8}-frac{15}{8}}=

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

Procijeni

$$\frac{3}{7}\approx 0,428571429$$

Koraci za rješenje

Saberite \frac{1}{3} i \frac{7}{9} da biste dobili \frac{10}{9}.

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

Izračunajte \frac{10}{9} stepen od 2 i dobijte \frac{100}{81}.

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

Oduzmite \frac{1}{2} od 1 da biste dobili \frac{1}{2}.

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

Izračunajte \frac{1}{2} stepen od 2 i dobijte \frac{1}{4}.

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

Izračunajte -2 stepen od 3 i dobijte -8.

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

Pomnožite \frac{1}{4} i -8 da biste dobili -2.

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

Oduzmite \frac{3}{2} od -2 da biste dobili -\frac{7}{2}.

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

Podijelite \frac{100}{81} sa -\frac{7}{2} tako što ćete pomnožiti \frac{100}{81} recipročnom vrijednošću od -\frac{7}{2}.

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

Pomnožite \frac{100}{81} i -\frac{2}{7} da biste dobili -\frac{200}{567}.

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

Opozit broja -\frac{200}{567} je \frac{200}{567}.

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

Izračunajte -\frac{1}{6} stepen od 2 i dobijte \frac{1}{36}.

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

Oduzmite \frac{1}{5} od \frac{1}{4} da biste dobili \frac{1}{20}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Oduzmite \frac{2}{5} od 1 da biste dobili \frac{3}{5}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Izračunajte \frac{3}{5} stepen od 2 i dobijte \frac{9}{25}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Podijelite \frac{1}{20} sa \frac{9}{25} tako što ćete pomnožiti \frac{1}{20} recipročnom vrijednošću od \frac{9}{25}.

$$\frac{200}{567}+\left(-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}\right)^{2}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Pomnožite \frac{1}{20} i \frac{25}{9} da biste dobili \frac{5}{36}.

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

Saberite -\frac{1}{36} i \frac{5}{36} da biste dobili \frac{1}{9}.

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

Izračunajte \frac{1}{9} stepen od 2 i dobijte \frac{1}{81}.

$$\frac{200}{567}+\frac{1}{81}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Saberite \frac{200}{567} i \frac{1}{81} da biste dobili \frac{23}{63}.

$$\frac{23}{63}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Oduzmite \frac{2}{9} od \frac{1}{3} da biste dobili \frac{1}{9}.

$$\frac{23}{63}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Oduzmite \frac{15}{8} od \frac{1}{8} da biste dobili -\frac{7}{4}.

$$\frac{23}{63}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

Podijelite \frac{1}{9} sa -\frac{7}{4} tako što ćete pomnožiti \frac{1}{9} recipročnom vrijednošću od -\frac{7}{4}.

$$\frac{23}{63}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

Pomnožite \frac{1}{9} i -\frac{4}{7} da biste dobili -\frac{4}{63}.

$$\frac{23}{63}-\left(-\frac{4}{63}\right)$$

Opozit broja -\frac{4}{63} je \frac{4}{63}.

$$\frac{23}{63}+\frac{4}{63}$$

Saberite \frac{23}{63} i \frac{4}{63} da biste dobili \frac{3}{7}.

$$\frac{3}{7}$$

Faktor

$$\frac{3}{7} = 0,42857142857142855$$