Whakaoti i te (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}}=

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

Aromātai

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

Ngā Upane Otinga

Tangohia te \frac{1}{2} i te 1, ka \frac{1}{2}.

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

Tātaihia te \frac{1}{2} mā te pū o 2, kia riro ko \frac{1}{4}.

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

Tātaihia te -2 mā te pū o 3, kia riro ko -8.

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

Whakareatia te \frac{1}{4} ki te -8, ka -2.

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

Tangohia te \frac{3}{2} i te -2, ka -\frac{7}{2}.

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

Tātaihia te -\frac{1}{6} mā te pū o 2, kia riro ko \frac{1}{36}.

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

Tangohia te \frac{1}{5} i te \frac{1}{4}, ka \frac{1}{20}.

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

Tangohia te \frac{2}{5} i te 1, ka \frac{3}{5}.

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

Tātaihia te \frac{3}{5} mā te pū o 2, kia riro ko \frac{9}{25}.

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

Whakawehe \frac{1}{20} ki te \frac{9}{25} mā te whakarea \frac{1}{20} ki te tau huripoki o \frac{9}{25}.

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

Whakareatia te \frac{1}{20} ki te \frac{25}{9}, ka \frac{5}{36}.

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

Tāpirihia te -\frac{1}{36} ki te \frac{5}{36}, ka \frac{1}{9}.

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

Ko te uara pū o tētahi tau tūturu a ko a ina a\geq 0, ko -a rānei ina a<0. Ko te uara pū o \frac{1}{9} ko \frac{1}{9}.

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

Tāpirihia te -\frac{7}{2} ki te \frac{1}{9}, ka -\frac{61}{18}.

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

Tangohia te \frac{2}{9} i te \frac{1}{3}, ka \frac{1}{9}.

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

Tangohia te \frac{15}{8} i te \frac{1}{8}, ka -\frac{7}{4}.

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

Whakawehe \frac{1}{9} ki te -\frac{7}{4} mā te whakarea \frac{1}{9} ki te tau huripoki o -\frac{7}{4}.

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

Whakareatia te \frac{1}{9} ki te -\frac{4}{7}, ka -\frac{4}{63}.

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

Ko te tauaro o -\frac{4}{63} ko \frac{4}{63}.

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

Tāpirihia te -\frac{61}{18} ki te \frac{4}{63}, ka -\frac{419}{126}.

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

Tauwehe

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