Whakaoti i te [(-1)^{3}div2/9+2^{200}*(-0.5)^200-3^3*(-3/2)^2]div|-4div2*(-1/2)^2|

$$[ ( - 1 ) ^ { 3 } \div \frac { 2 } { 9 } + 2 ^ { 200 } \times ( - 0.5 ) ^ { 200 } - 3 ^ { 3 } \times ( - \frac { 3 } { 2 } ) ^ { 2 } ] \div | - 4 \div 2 \times ( - \frac { 1 } { 2 } ) ^ { 2 } |$$

Aromātai

$$-128.5$$

Ngā Upane Otinga

Tātaihia te -1 mā te pū o 3, kia riro ko -1.

$$\frac{\frac{-1}{\frac{2}{9}}+2^{200}\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Whakawehe -1 ki te \frac{2}{9} mā te whakarea -1 ki te tau huripoki o \frac{2}{9}.

$$\frac{-\frac{9}{2}+2^{200}\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tātaihia te 2 mā te pū o 200, kia riro ko 1606938044258990275541962092341162602522202993782792835301376.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\left(-0.5\right)^{200}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tātaihia te -0.5 mā te pū o 200, kia riro ko 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625.

$$\frac{-\frac{9}{2}+1606938044258990275541962092341162602522202993782792835301376\times 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Whakareatia te 1606938044258990275541962092341162602522202993782792835301376 ki te 0.00000000000000000000000000000000000000000000000000000000000062230152778611417071440640537801242405902521687211671331011166147896988340353834411839448231257136169569665895551224821247160434722900390625, ka 1.

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

Me tahuri te 1 ki te hautau \frac{2}{2}.

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

Tā te mea he rite te tauraro o -\frac{9}{2} me \frac{2}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te -9 ki te 2, ka -7.

$$\frac{-\frac{7}{2}-3^{3}\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tātaihia te 3 mā te pū o 3, kia riro ko 27.

$$\frac{-\frac{7}{2}-27\left(-\frac{3}{2}\right)^{2}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tātaihia te -\frac{3}{2} mā te pū o 2, kia riro ko \frac{9}{4}.

$$\frac{-\frac{7}{2}-27\times \frac{9}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tuhia te 27\times \frac{9}{4} hei hautanga kotahi.

$$\frac{-\frac{7}{2}-\frac{27\times 9}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Whakareatia te 27 ki te 9, ka 243.

$$\frac{-\frac{7}{2}-\frac{243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri -\frac{7}{2} me \frac{243}{4} ki te hautau me te tautūnga 4.

$$\frac{-\frac{14}{4}-\frac{243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tā te mea he rite te tauraro o -\frac{14}{4} me \frac{243}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{-14-243}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Tangohia te 243 i te -14, ka -257.

$$\frac{-\frac{257}{4}}{|\frac{-4}{2}\left(-\frac{1}{2}\right)^{2}|}$$

Whakawehea te -4 ki te 2, kia riro ko -2.

$$\frac{-\frac{257}{4}}{|-2\left(-\frac{1}{2}\right)^{2}|}$$

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

$$\frac{-\frac{257}{4}}{|-2\times \frac{1}{4}|}$$

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

$$\frac{-\frac{257}{4}}{|\frac{-2}{4}|}$$

Whakahekea te hautanga \frac{-2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{-\frac{257}{4}}{|-\frac{1}{2}|}$$

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}{2} ko \frac{1}{2}.

$$\frac{-\frac{257}{4}}{\frac{1}{2}}$$

Whakawehe -\frac{257}{4} ki te \frac{1}{2} mā te whakarea -\frac{257}{4} ki te tau huripoki o \frac{1}{2}.

$$-\frac{257}{4}\times 2$$

Tuhia te -\frac{257}{4}\times 2 hei hautanga kotahi.

$$\frac{-257\times 2}{4}$$

Whakareatia te -257 ki te 2, ka -514.

$$\frac{-514}{4}$$

Whakahekea te hautanga \frac{-514}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{257}{2}$$

Tauwehe

$$-128.5$$