Whakaoti i te 1/22.718^4+2.718^3/2.718^2-2*2.718+1-2.7718^2

$$\frac{ \frac{ 1 }{ 2 } { 2.718 }^{ 4 } + { 2.718 }^{ 3 } }{ { 2.718 }^{ 2 } -2 \cdot 2.718+1 } - { 2.7718 }^{ 2 }$$

Aromātai

$$\frac{154317843733889}{18447025000000}\approx 8.365459674$$

Ngā Upane Otinga

Tātaihia te 2.718 mā te pū o 4, kia riro ko 54.575510850576.

$$\frac{\frac{1}{2}\times 54.575510850576+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Me tahuri ki tau ā-ira 54.575510850576 ki te hautau \frac{13643877712644}{10000000000}. Whakahekea te hautanga \frac{13643877712644}{10000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{\frac{1}{2}\times \frac{3410969428161}{62500000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Me whakarea te \frac{1}{2} ki te \frac{3410969428161}{62500000000} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{1\times 3410969428161}{2\times 62500000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3410969428161}{2\times 62500000000}.

$$\frac{\frac{3410969428161}{125000000000}+2.718^{3}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Tātaihia te 2.718 mā te pū o 3, kia riro ko 20.079290232.

$$\frac{\frac{3410969428161}{125000000000}+20.079290232}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Me tahuri ki tau ā-ira 20.079290232 ki te hautau \frac{20079290232}{1000000000}. Whakahekea te hautanga \frac{20079290232}{1000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$\frac{\frac{3410969428161}{125000000000}+\frac{2509911279}{125000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Ko te maha noa iti rawa atu o 125000000000 me 125000000 ko 125000000000. Me tahuri \frac{3410969428161}{125000000000} me \frac{2509911279}{125000000} ki te hautau me te tautūnga 125000000000.

$$\frac{\frac{3410969428161}{125000000000}+\frac{2509911279000}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Tā te mea he rite te tauraro o \frac{3410969428161}{125000000000} me \frac{2509911279000}{125000000000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{3410969428161+2509911279000}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Tāpirihia te 3410969428161 ki te 2509911279000, ka 5920880707161.

$$\frac{\frac{5920880707161}{125000000000}}{2.718^{2}-2\times 2.718+1}-2.7718^{2}$$

Tātaihia te 2.718 mā te pū o 2, kia riro ko 7.387524.

$$\frac{\frac{5920880707161}{125000000000}}{7.387524-2\times 2.718+1}-2.7718^{2}$$

Whakareatia te 2 ki te 2.718, ka 5.436.

$$\frac{\frac{5920880707161}{125000000000}}{7.387524-5.436+1}-2.7718^{2}$$

Tangohia te 5.436 i te 7.387524, ka 1.951524.

$$\frac{\frac{5920880707161}{125000000000}}{1.951524+1}-2.7718^{2}$$

Tāpirihia te 1.951524 ki te 1, ka 2.951524.

$$\frac{\frac{5920880707161}{125000000000}}{2.951524}-2.7718^{2}$$

Tuhia te \frac{\frac{5920880707161}{125000000000}}{2.951524} hei hautanga kotahi.

$$\frac{5920880707161}{125000000000\times 2.951524}-2.7718^{2}$$

Whakareatia te 125000000000 ki te 2.951524, ka 368940500000.

$$\frac{5920880707161}{368940500000}-2.7718^{2}$$

Tātaihia te 2.7718 mā te pū o 2, kia riro ko 7.68287524.

$$\frac{5920880707161}{368940500000}-7.68287524$$

Me tahuri ki tau ā-ira 7.68287524 ki te hautau \frac{768287524}{100000000}. Whakahekea te hautanga \frac{768287524}{100000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{5920880707161}{368940500000}-\frac{192071881}{25000000}$$

Ko te maha noa iti rawa atu o 368940500000 me 25000000 ko 18447025000000. Me tahuri \frac{5920880707161}{368940500000} me \frac{192071881}{25000000} ki te hautau me te tautūnga 18447025000000.

$$\frac{296044035358050}{18447025000000}-\frac{141726191624161}{18447025000000}$$

Tā te mea he rite te tauraro o \frac{296044035358050}{18447025000000} me \frac{141726191624161}{18447025000000}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{296044035358050-141726191624161}{18447025000000}$$

Tangohia te 141726191624161 i te 296044035358050, ka 154317843733889.

$$\frac{154317843733889}{18447025000000}$$

Tauwehe

$$\frac{11 \cdot 29 \cdot 61 \cdot 7930409771}{2 ^ {6} \cdot 5 ^ {8} \cdot 859 ^ {2}} = 8\frac{6741643733889}{18447025000000} = 8.365459673518576$$