Whakaoti i te 27^frac{4{3}}+(sqrt{243}4/5)div(sqrt{125})^frac{9{9}}

$$27 ^ { \frac { 4 } { 3 } } + ( \sqrt { 243 } \frac { 4 } { 5 } ) \div ( \sqrt { 125 } ) ^ { \frac { 9 } { 9 } }$$

Aromātai

$$\frac{36\sqrt{15}}{125}+81\approx 82.115419204$$

Ngā Hipanga Rongoā Poto

Whakawehea te 9 ki te 9, kia riro ko 1.

$$27^{\frac{4}{3}}+\frac{\sqrt{243}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Tātaihia te 27 mā te pū o \frac{4}{3}, kia riro ko 81.

$$81+\frac{\sqrt{243}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Tauwehea te 243=9^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{9^{2}\times 3} hei hua o ngā pūtake rua \sqrt{9^{2}}\sqrt{3}. Tuhia te pūtakerua o te 9^{2}.

$$81+\frac{9\sqrt{3}\times \frac{4}{5}}{\left(\sqrt{125}\right)^{1}}$$

Whakareatia te 9 ki te \frac{4}{5}, ka \frac{36}{5}.

$$81+\frac{\frac{36}{5}\sqrt{3}}{\left(\sqrt{125}\right)^{1}}$$

Tātaihia te \sqrt{125} mā te pū o 1, kia riro ko \sqrt{125}.

$$81+\frac{\frac{36}{5}\sqrt{3}}{\sqrt{125}}$$

Whakangāwaritia te tauraro o \frac{\frac{36}{5}\sqrt{3}}{\sqrt{125}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{125}.

$$81+\frac{\frac{36}{5}\sqrt{3}\sqrt{125}}{\left(\sqrt{125}\right)^{2}}$$

Ko te pūrua o \sqrt{125} ko 125.

$$81+\frac{\frac{36}{5}\sqrt{3}\sqrt{125}}{125}$$

Tauwehea te 125=5^{2}\times 5. Tuhia anō te pūtake rua o te hua \sqrt{5^{2}\times 5} hei hua o ngā pūtake rua \sqrt{5^{2}}\sqrt{5}. Tuhia te pūtakerua o te 5^{2}.

$$81+\frac{\frac{36}{5}\sqrt{3}\times 5\sqrt{5}}{125}$$

Whakareatia te \frac{36}{5} ki te 5, ka 36.

$$81+\frac{36\sqrt{3}\sqrt{5}}{125}$$

Hei whakarea \sqrt{3} me \sqrt{5}, whakareatia ngā tau i raro i te pūtake rua.

$$81+\frac{36\sqrt{15}}{125}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 81 ki te \frac{125}{125}.

$$\frac{81\times 125}{125}+\frac{36\sqrt{15}}{125}$$

Tā te mea he rite te tauraro o \frac{81\times 125}{125} me \frac{36\sqrt{15}}{125}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{81\times 125+36\sqrt{15}}{125}$$

Mahia ngā whakarea i roto o 81\times 125+36\sqrt{15}.

$$\frac{10125+36\sqrt{15}}{125}$$

Tauwehe

$$\frac{9 {(4 \sqrt{15} + 1125)}}{125} = 82.11541920370775$$