Whakaoti i te -5/4+5/2*[(-3/5)^2-(1/2)^4*(-32)]div(-2frac{4}{5})

$$- \frac { 5 } { 4 } + \frac { 5 } { 2 } \times [ ( - \frac { 3 } { 5 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 4 } \times ( - 32 ) ] \div ( - 2 \frac { 4 } { 5 } )$$

Aromātai

$$-\frac{47}{14}\approx -3.357142857$$

Ngā Upane Otinga

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

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(\frac{1}{2}\right)^{4}\left(-32\right)\right)}{-\frac{2\times 5+4}{5}}$$

Tātaihia te \frac{1}{2} mā te pū o 4, kia riro ko \frac{1}{16}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{1}{16}\left(-32\right)\right)}{-\frac{2\times 5+4}{5}}$$

Whakareatia te \frac{1}{16} ki te -32, ka \frac{-32}{16}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{-32}{16}\right)}{-\frac{2\times 5+4}{5}}$$

Whakawehea te -32 ki te 16, kia riro ko -2.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(-2\right)\right)}{-\frac{2\times 5+4}{5}}$$

Ko te tauaro o -2 ko 2.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+2\right)}{-\frac{2\times 5+4}{5}}$$

Me tahuri te 2 ki te hautau \frac{50}{25}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+\frac{50}{25}\right)}{-\frac{2\times 5+4}{5}}$$

Tā te mea he rite te tauraro o \frac{9}{25} me \frac{50}{25}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{9+50}{25}}{-\frac{2\times 5+4}{5}}$$

Tāpirihia te 9 ki te 50, ka 59.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{59}{25}}{-\frac{2\times 5+4}{5}}$$

Me whakarea te \frac{5}{2} ki te \frac{59}{25} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$-\frac{5}{4}+\frac{\frac{5\times 59}{2\times 25}}{-\frac{2\times 5+4}{5}}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 59}{2\times 25}.

$$-\frac{5}{4}+\frac{\frac{295}{50}}{-\frac{2\times 5+4}{5}}$$

Whakahekea te hautanga \frac{295}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{2\times 5+4}{5}}$$

Whakareatia te 2 ki te 5, ka 10.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{10+4}{5}}$$

Tāpirihia te 10 ki te 4, ka 14.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{14}{5}}$$

Whakawehe \frac{59}{10} ki te -\frac{14}{5} mā te whakarea \frac{59}{10} ki te tau huripoki o -\frac{14}{5}.

$$-\frac{5}{4}+\frac{59}{10}\left(-\frac{5}{14}\right)$$

Me whakarea te \frac{59}{10} ki te -\frac{5}{14} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$-\frac{5}{4}+\frac{59\left(-5\right)}{10\times 14}$$

Mahia ngā whakarea i roto i te hautanga \frac{59\left(-5\right)}{10\times 14}.

$$-\frac{5}{4}+\frac{-295}{140}$$

Whakahekea te hautanga \frac{-295}{140} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$-\frac{5}{4}-\frac{59}{28}$$

Ko te maha noa iti rawa atu o 4 me 28 ko 28. Me tahuri -\frac{5}{4} me \frac{59}{28} ki te hautau me te tautūnga 28.

$$-\frac{35}{28}-\frac{59}{28}$$

Tā te mea he rite te tauraro o -\frac{35}{28} me \frac{59}{28}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-35-59}{28}$$

Tangohia te 59 i te -35, ka -94.

$$\frac{-94}{28}$$

Whakahekea te hautanga \frac{-94}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{47}{14}$$

Tauwehe

$$-\frac{47}{14} = -3\frac{5}{14} = -3.357142857142857$$