Lutasin ang (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}}=

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

I-evaluate

$$-\frac{101}{567}\approx -0.178130511$$

Mga Hakbang ng Solution

Idagdag ang \frac{1}{3} at \frac{7}{9} para makuha ang \frac{10}{9}.

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

Kalkulahin ang \frac{10}{9} sa power ng 2 at kunin ang \frac{100}{81}.

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

I-subtract ang \frac{1}{2} mula sa 1 para makuha ang \frac{1}{2}.

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

Kalkulahin ang \frac{1}{2} sa power ng 2 at kunin ang \frac{1}{4}.

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

Kalkulahin ang -2 sa power ng 3 at kunin ang -8.

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

I-multiply ang \frac{1}{4} at -8 para makuha ang -2.

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

I-subtract ang \frac{3}{2} mula sa -2 para makuha ang -\frac{7}{2}.

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

I-divide ang \frac{100}{81} gamit ang -\frac{7}{2} sa pamamagitan ng pagmu-multiply sa \frac{100}{81} gamit ang reciprocal ng -\frac{7}{2}.

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

I-multiply ang \frac{100}{81} at -\frac{2}{7} para makuha ang -\frac{200}{567}.

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

Kalkulahin ang -\frac{1}{6} sa power ng 2 at kunin ang \frac{1}{36}.

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

I-subtract ang \frac{1}{36} mula sa -\frac{200}{567} para makuha ang -\frac{863}{2268}.

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

I-subtract ang \frac{1}{5} mula sa \frac{1}{4} para makuha ang \frac{1}{20}.

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

I-subtract ang \frac{2}{5} mula sa 1 para makuha ang \frac{3}{5}.

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

Kalkulahin ang \frac{3}{5} sa power ng 2 at kunin ang \frac{9}{25}.

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

I-divide ang \frac{1}{20} gamit ang \frac{9}{25} sa pamamagitan ng pagmu-multiply sa \frac{1}{20} gamit ang reciprocal ng \frac{9}{25}.

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

I-multiply ang \frac{1}{20} at \frac{25}{9} para makuha ang \frac{5}{36}.

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

Idagdag ang -\frac{863}{2268} at \frac{5}{36} para makuha ang -\frac{137}{567}.

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

I-subtract ang \frac{2}{9} mula sa \frac{1}{3} para makuha ang \frac{1}{9}.

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

I-subtract ang \frac{15}{8} mula sa \frac{1}{8} para makuha ang -\frac{7}{4}.

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

I-divide ang \frac{1}{9} gamit ang -\frac{7}{4} sa pamamagitan ng pagmu-multiply sa \frac{1}{9} gamit ang reciprocal ng -\frac{7}{4}.

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

I-multiply ang \frac{1}{9} at -\frac{4}{7} para makuha ang -\frac{4}{63}.

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

Ang kabaliktaran ng -\frac{4}{63} ay \frac{4}{63}.

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

Idagdag ang -\frac{137}{567} at \frac{4}{63} para makuha ang -\frac{101}{567}.

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

I-factor

$$-\frac{101}{567} = -0.1781305114638448$$