Whakaoti i te {left(1/2right)}^2left({left(1/2right)}^2-1/2+1right)left({left(1/2right)}^3-{left(frac{1}{2}right)}^2+frac{1}{2}-1right)

$${ \left( \frac{ 1 }{ 2 } \right) }^{ 2 } \left( { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } - \frac{ 1 }{ 2 } +1 \right) \left( { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } - { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } + \frac{ 1 }{ 2 } -1 \right)$$

Aromātai

$$-\frac{15}{128}=-0.1171875$$

Ngā Upane Otinga

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

$$\frac{1}{4}\left(\left(\frac{1}{2}\right)^{2}-\frac{1}{2}+1\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

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

$$\frac{1}{4}\left(\frac{1}{4}-\frac{1}{2}+1\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{1}{4} me \frac{1}{2} ki te hautau me te tautūnga 4.

$$\frac{1}{4}\left(\frac{1}{4}-\frac{2}{4}+1\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Tā te mea he rite te tauraro o \frac{1}{4} me \frac{2}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{4}\left(\frac{1-2}{4}+1\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Tangohia te 2 i te 1, ka -1.

$$\frac{1}{4}\left(-\frac{1}{4}+1\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{1}{4}\left(-\frac{1}{4}+\frac{4}{4}\right)\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Tā te mea he rite te tauraro o -\frac{1}{4} me \frac{4}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{4}\times \frac{-1+4}{4}\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Tāpirihia te -1 ki te 4, ka 3.

$$\frac{1}{4}\times \frac{3}{4}\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Me whakarea te \frac{1}{4} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1\times 3}{4\times 4}\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{4\times 4}.

$$\frac{3}{16}\left(\left(\frac{1}{2}\right)^{3}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

Tātaihia te \frac{1}{2} mā te pū o 3, kia riro ko \frac{1}{8}.

$$\frac{3}{16}\left(\frac{1}{8}-\left(\frac{1}{2}\right)^{2}+\frac{1}{2}-1\right)$$

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

$$\frac{3}{16}\left(\frac{1}{8}-\frac{1}{4}+\frac{1}{2}-1\right)$$

Ko te maha noa iti rawa atu o 8 me 4 ko 8. Me tahuri \frac{1}{8} me \frac{1}{4} ki te hautau me te tautūnga 8.

$$\frac{3}{16}\left(\frac{1}{8}-\frac{2}{8}+\frac{1}{2}-1\right)$$

Tā te mea he rite te tauraro o \frac{1}{8} me \frac{2}{8}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{16}\left(\frac{1-2}{8}+\frac{1}{2}-1\right)$$

Tangohia te 2 i te 1, ka -1.

$$\frac{3}{16}\left(-\frac{1}{8}+\frac{1}{2}-1\right)$$

Ko te maha noa iti rawa atu o 8 me 2 ko 8. Me tahuri -\frac{1}{8} me \frac{1}{2} ki te hautau me te tautūnga 8.

$$\frac{3}{16}\left(-\frac{1}{8}+\frac{4}{8}-1\right)$$

Tā te mea he rite te tauraro o -\frac{1}{8} me \frac{4}{8}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3}{16}\left(\frac{-1+4}{8}-1\right)$$

Tāpirihia te -1 ki te 4, ka 3.

$$\frac{3}{16}\left(\frac{3}{8}-1\right)$$

Me tahuri te 1 ki te hautau \frac{8}{8}.

$$\frac{3}{16}\left(\frac{3}{8}-\frac{8}{8}\right)$$

Tā te mea he rite te tauraro o \frac{3}{8} me \frac{8}{8}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{16}\times \frac{3-8}{8}$$

Tangohia te 8 i te 3, ka -5.

$$\frac{3}{16}\left(-\frac{5}{8}\right)$$

Me whakarea te \frac{3}{16} ki te -\frac{5}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3\left(-5\right)}{16\times 8}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\left(-5\right)}{16\times 8}.

$$\frac{-15}{128}$$

Ka taea te hautanga \frac{-15}{128} te tuhi anō ko -\frac{15}{128} mā te tango i te tohu tōraro.

$$-\frac{15}{128}$$

Tauwehe

$$-\frac{15}{128} = -0.1171875$$