Whakaoti i te (5^{-1})^{-2}*(2^{4}*5^7)div(2^2*5^2)^5

$$( 5 ^ { - 1 } ) ^ { - 2 } \cdot ( 2 ^ { 4 } \cdot 5 ^ { 7 } ) \div ( 2 ^ { 2 } \cdot 5 ^ { 2 } ) ^ { 5 }$$

Aromātai

$$\frac{1}{320}=0.003125$$

Ngā Upane Otinga

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te -1 me te -2 kia riro ai te 2.

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

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 7 kia riro ai te 9.

$$\frac{5^{9}\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Tātaihia te 5 mā te pū o 9, kia riro ko 1953125.

$$\frac{1953125\times 2^{4}}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Tātaihia te 2 mā te pū o 4, kia riro ko 16.

$$\frac{1953125\times 16}{\left(2^{2}\times 5^{2}\right)^{5}}$$

Whakareatia te 1953125 ki te 16, ka 31250000.

$$\frac{31250000}{\left(2^{2}\times 5^{2}\right)^{5}}$$

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

$$\frac{31250000}{\left(4\times 5^{2}\right)^{5}}$$

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

$$\frac{31250000}{\left(4\times 25\right)^{5}}$$

Whakareatia te 4 ki te 25, ka 100.

$$\frac{31250000}{100^{5}}$$

Tātaihia te 100 mā te pū o 5, kia riro ko 10000000000.

$$\frac{31250000}{10000000000}$$

Whakahekea te hautanga \frac{31250000}{10000000000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 31250000.

$$\frac{1}{320}$$

Tauwehe

$$\frac{1}{2 ^ {6} \cdot 5} = 0.003125$$