Lutasin ang (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}}=

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

I-evaluate

$$-\frac{419}{126}\approx -3.325396825$$

Mga Hakbang ng Solution

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

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

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

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

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

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

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

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

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

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

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

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

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

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(1-\frac{2}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\left(\frac{3}{5}\right)^{2}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{\frac{1}{20}}{\frac{9}{25}}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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}.

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{1}{20}\times \frac{25}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{7}{2}+|-\frac{1}{36}+\frac{5}{36}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Idagdag ang -\frac{1}{36} at \frac{5}{36} para makuha ang \frac{1}{9}.

$$-\frac{7}{2}+|\frac{1}{9}|-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Ang absolute value ng isang real number na a ay a kapag a\geq 0, o -a kapag a<0. Ang absolute value ng \frac{1}{9} ay \frac{1}{9}.

$$-\frac{7}{2}+\frac{1}{9}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

Idagdag ang -\frac{7}{2} at \frac{1}{9} para makuha ang -\frac{61}{18}.

$$-\frac{61}{18}-\frac{\frac{1}{3}-\frac{2}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{61}{18}-\frac{\frac{1}{9}}{\frac{1}{8}-\frac{15}{8}}$$

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

$$-\frac{61}{18}-\frac{\frac{1}{9}}{-\frac{7}{4}}$$

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}.

$$-\frac{61}{18}-\frac{1}{9}\left(-\frac{4}{7}\right)$$

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

$$-\frac{61}{18}-\left(-\frac{4}{63}\right)$$

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

$$-\frac{61}{18}+\frac{4}{63}$$

Idagdag ang -\frac{61}{18} at \frac{4}{63} para makuha ang -\frac{419}{126}.

$$-\frac{419}{126}$$

I-factor

$$-\frac{419}{126} = -3\frac{41}{126} = -3.3253968253968256$$