Whakaoti i te ((-1/4)^{3}:(-1/4)+(2-1/2)^{4}(1-5/9)^2):[(frac{17}{2})^4:(frac{17}{2})^3+frac{3}{2}*(-1)^2-1+frac{1}{4}]*frac{37}{2}

$$( ( - \frac { 1 } { 4 } ) ^ { 3 } : ( - \frac { 1 } { 4 } ) + ( 2 - \frac { 1 } { 2 } ) ^ { 4 } ( 1 - \frac { 5 } { 9 } ) ^ { 2 } ) : [ ( \frac { 17 } { 2 } ) ^ { 4 } : ( \frac { 17 } { 2 } ) ^ { 3 } + \frac { 3 } { 2 } \cdot ( - 1 ) ^ { 2 } - 1 + \frac { 1 } { 4 } ] \cdot \frac { 37 } { 2 }$$

Aromātai

$$\frac{17}{8}=2.125$$

Ngā Upane Otinga

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 3 kia riro ai te 2.

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\frac{\left(\frac{17}{2}\right)^{4}}{\left(\frac{17}{2}\right)^{3}}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

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

$$\frac{\left(-\frac{1}{4}\right)^{2}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

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

$$\frac{\frac{1}{16}+\left(2-\frac{1}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tangohia te \frac{1}{2} i te 2, ka \frac{3}{2}.

$$\frac{\frac{1}{16}+\left(\frac{3}{2}\right)^{4}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tātaihia te \frac{3}{2} mā te pū o 4, kia riro ko \frac{81}{16}.

$$\frac{\frac{1}{16}+\frac{81}{16}\left(1-\frac{5}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tangohia te \frac{5}{9} i te 1, ka \frac{4}{9}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \left(\frac{4}{9}\right)^{2}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tātaihia te \frac{4}{9} mā te pū o 2, kia riro ko \frac{16}{81}.

$$\frac{\frac{1}{16}+\frac{81}{16}\times \frac{16}{81}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Whakareatia te \frac{81}{16} ki te \frac{16}{81}, ka 1.

$$\frac{\frac{1}{16}+1}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tāpirihia te \frac{1}{16} ki te 1, ka \frac{17}{16}.

$$\frac{\frac{17}{16}}{\left(\frac{17}{2}\right)^{1}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tātaihia te \frac{17}{2} mā te pū o 1, kia riro ko \frac{17}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\left(-1\right)^{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tātaihia te -1 mā te pū o 2, kia riro ko 1.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}\times 1-1+\frac{1}{4}}\times \frac{37}{2}$$

Whakareatia te \frac{3}{2} ki te 1, ka \frac{3}{2}.

$$\frac{\frac{17}{16}}{\frac{17}{2}+\frac{3}{2}-1+\frac{1}{4}}\times \frac{37}{2}$$

Tāpirihia te \frac{17}{2} ki te \frac{3}{2}, ka 10.

$$\frac{\frac{17}{16}}{10-1+\frac{1}{4}}\times \frac{37}{2}$$

Tangohia te 1 i te 10, ka 9.

$$\frac{\frac{17}{16}}{9+\frac{1}{4}}\times \frac{37}{2}$$

Tāpirihia te 9 ki te \frac{1}{4}, ka \frac{37}{4}.

$$\frac{\frac{17}{16}}{\frac{37}{4}}\times \frac{37}{2}$$

Whakawehe \frac{17}{16} ki te \frac{37}{4} mā te whakarea \frac{17}{16} ki te tau huripoki o \frac{37}{4}.

$$\frac{17}{16}\times \frac{4}{37}\times \frac{37}{2}$$

Whakareatia te \frac{17}{16} ki te \frac{4}{37}, ka \frac{17}{148}.

$$\frac{17}{148}\times \frac{37}{2}$$

Whakareatia te \frac{17}{148} ki te \frac{37}{2}, ka \frac{17}{8}.

$$\frac{17}{8}$$

Tauwehe

$$\frac{17}{2 ^ {3}} = 2\frac{1}{8} = 2.125$$