Whakaoti i te (4^{2})^{2}:(4^{10}:4^{9})-[(2+2^{2}*9)*3-6*3^{2}]+5^7:(2^2+1)^5-2*2^2

$$( 4 ^ { 2 } ) ^ { 2 } : ( 4 ^ { 10 } : 4 ^ { 9 } ) - [ ( 2 + 2 ^ { 2 } \times 9 ) \times 3 - 6 \times 3 ^ { 2 } ] + 5 ^ { 7 } : ( 2 ^ { 2 } + 1 ) ^ { 5 } - 2 \times 2 ^ { 2 }$$

Aromātai

$$21$$

Ngā Upane Otinga

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 2 kia riro ai te 4.

$$\frac{4^{4}}{\frac{4^{10}}{4^{9}}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 9 i te 10 kia riro ai te 1.

$$\frac{4^{4}}{4^{1}}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

Hei whakawehe ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga. Me tango te 1 i te 4 kia riro ai te 3.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2\times 2^{2}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 1 me te 2 kia riro ai te 3.

$$4^{3}-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tātaihia te 4 mā te pū o 3, kia riro ko 64.

$$64-\left(\left(2+2^{2}\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

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

$$64-\left(\left(2+4\times 9\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Whakareatia te 4 ki te 9, ka 36.

$$64-\left(\left(2+36\right)\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tāpirihia te 2 ki te 36, ka 38.

$$64-\left(38\times 3-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Whakareatia te 38 ki te 3, ka 114.

$$64-\left(114-6\times 3^{2}\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tātaihia te 3 mā te pū o 2, kia riro ko 9.

$$64-\left(114-6\times 9\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Whakareatia te 6 ki te 9, ka 54.

$$64-\left(114-54\right)+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tangohia te 54 i te 114, ka 60.

$$64-60+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tangohia te 60 i te 64, ka 4.

$$4+\frac{5^{7}}{\left(2^{2}+1\right)^{5}}-2^{3}$$

Tātaihia te 5 mā te pū o 7, kia riro ko 78125.

$$4+\frac{78125}{\left(2^{2}+1\right)^{5}}-2^{3}$$

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

$$4+\frac{78125}{\left(4+1\right)^{5}}-2^{3}$$

Tāpirihia te 4 ki te 1, ka 5.

$$4+\frac{78125}{5^{5}}-2^{3}$$

Tātaihia te 5 mā te pū o 5, kia riro ko 3125.

$$4+\frac{78125}{3125}-2^{3}$$

Whakawehea te 78125 ki te 3125, kia riro ko 25.

$$4+25-2^{3}$$

Tāpirihia te 4 ki te 25, ka 29.

$$29-2^{3}$$

Tātaihia te 2 mā te pū o 3, kia riro ko 8.

$$29-8$$

Tangohia te 8 i te 29, ka 21.

$$21$$

Tauwehe

$$3\times 7$$