Whakaoti i te [(-2/5)^{2}*(1/4)^{2}]^{2}:(5^{2}*2^{2})^-2-(4/5)^-5*(-4/5)^-4:(frac{4}{5})^-7

$$[ ( - \frac { 2 } { 5 } ) ^ { 2 } \cdot ( \frac { 1 } { 4 } ) ^ { 2 } ] ^ { 2 } : ( 5 ^ { 2 } \cdot 2 ^ { 2 } ) ^ { - 2 } - ( \frac { 4 } { 5 } ) ^ { - 5 } \cdot ( - \frac { 4 } { 5 } ) ^ { - 4 } : ( \frac { 4 } { 5 } ) ^ { - 7 }$$

Aromātai

$$-\frac{9}{16}=-0.5625$$

Ngā Upane Otinga

Tātaihia te -\frac{2}{5} mā te pū o 2, kia riro ko \frac{4}{25}.

$$\frac{\left(\frac{4}{25}\times \left(\frac{1}{4}\right)^{2}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

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

$$\frac{\left(\frac{4}{25}\times \frac{1}{16}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Whakareatia te \frac{4}{25} ki te \frac{1}{16}, ka \frac{1}{100}.

$$\frac{\left(\frac{1}{100}\right)^{2}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Tātaihia te \frac{1}{100} mā te pū o 2, kia riro ko \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\left(5^{2}\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{\frac{1}{10000}}{\left(25\times 2^{2}\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Tātaihia te 2 mā te pū o 2, kia riro ko 4.

$$\frac{\frac{1}{10000}}{\left(25\times 4\right)^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Whakareatia te 25 ki te 4, ka 100.

$$\frac{\frac{1}{10000}}{100^{-2}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Tātaihia te 100 mā te pū o -2, kia riro ko \frac{1}{10000}.

$$\frac{\frac{1}{10000}}{\frac{1}{10000}}-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Whakawehea te \frac{1}{10000} ki te \frac{1}{10000}, kia riro ko 1.

$$1-\frac{\left(\frac{4}{5}\right)^{-5}\left(-\frac{4}{5}\right)^{-4}}{\left(\frac{4}{5}\right)^{-7}}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

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

Tātaihia te -\frac{4}{5} mā te pū o -4, kia riro ko \frac{625}{256}.

$$1-\frac{625}{256}\times \left(\frac{4}{5}\right)^{2}$$

Tātaihia te \frac{4}{5} mā te pū o 2, kia riro ko \frac{16}{25}.

$$1-\frac{625}{256}\times \frac{16}{25}$$

Whakareatia te \frac{625}{256} ki te \frac{16}{25}, ka \frac{25}{16}.

$$1-\frac{25}{16}$$

Tangohia te \frac{25}{16} i te 1, ka -\frac{9}{16}.

$$-\frac{9}{16}$$

Tauwehe

$$-\frac{9}{16} = -0.5625$$