Whakaoti i te [(2/3)^{2}*(-2/3)^{3}*(-2/3)^{4}]^{2}:[-(-2/3)^{5}]^3+(-frac{2}{3})^3-(frac{2}{7})^4*(-frac{7}{4})^4

$$[ ( \frac { 2 } { 3 } ) ^ { 2 } \cdot ( - \frac { 2 } { 3 } ) ^ { 3 } \cdot ( - \frac { 2 } { 3 } ) ^ { 4 } ] ^ { 2 } : [ - ( - \frac { 2 } { 3 } ) ^ { 5 } ] ^ { 3 } + ( - \frac { 2 } { 3 } ) ^ { 3 } - ( \frac { 2 } { 7 } ) ^ { 4 } \cdot ( - \frac { 7 } { 4 } ) ^ { 4 }$$

Aromātai

$$-\frac{1}{16}=-0.0625$$

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 4 kia riro ai te 7.

$$\frac{\left(\left(\frac{2}{3}\right)^{2}\left(-\frac{2}{3}\right)^{7}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

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

$$\frac{\left(\frac{4}{9}\left(-\frac{2}{3}\right)^{7}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te -\frac{2}{3} mā te pū o 7, kia riro ko -\frac{128}{2187}.

$$\frac{\left(\frac{4}{9}\left(-\frac{128}{2187}\right)\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Whakareatia te \frac{4}{9} ki te -\frac{128}{2187}, ka -\frac{512}{19683}.

$$\frac{\left(-\frac{512}{19683}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te -\frac{512}{19683} mā te pū o 2, kia riro ko \frac{262144}{387420489}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te -\frac{2}{3} mā te pū o 5, kia riro ko -\frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{32}{243}\right)\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Ko te tauaro o -\frac{32}{243} ko \frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(\frac{32}{243}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te \frac{32}{243} mā te pū o 3, kia riro ko \frac{32768}{14348907}.

$$\frac{\frac{262144}{387420489}}{\frac{32768}{14348907}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Whakawehe \frac{262144}{387420489} ki te \frac{32768}{14348907} mā te whakarea \frac{262144}{387420489} ki te tau huripoki o \frac{32768}{14348907}.

$$\frac{262144}{387420489}\times \frac{14348907}{32768}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Whakareatia te \frac{262144}{387420489} ki te \frac{14348907}{32768}, ka \frac{8}{27}.

$$\frac{8}{27}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te -\frac{2}{3} mā te pū o 3, kia riro ko -\frac{8}{27}.

$$\frac{8}{27}-\frac{8}{27}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tangohia te \frac{8}{27} i te \frac{8}{27}, ka 0.

$$0-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te \frac{2}{7} mā te pū o 4, kia riro ko \frac{16}{2401}.

$$0-\frac{16}{2401}\left(-\frac{7}{4}\right)^{4}$$

Tātaihia te -\frac{7}{4} mā te pū o 4, kia riro ko \frac{2401}{256}.

$$0-\frac{16}{2401}\times \frac{2401}{256}$$

Whakareatia te \frac{16}{2401} ki te \frac{2401}{256}, ka \frac{1}{16}.

$$0-\frac{1}{16}$$

Tangohia te \frac{1}{16} i te 0, ka -\frac{1}{16}.

$$-\frac{1}{16}$$

Tauwehe

$$-\frac{1}{16} = -0.0625$$