Whakaoti i te a1-1/8^6/1-frac{1{3^2}}=2457

$$a \frac { 1 - \frac { 1 } { 8 ^ { 6 } } } { 1 - \frac { 1 } { 3 ^ { 2 } } } = 2457$$

Whakaoti mō a

$$a = \frac{27262976}{12483} = 2184\frac{104}{12483} \approx 2184.008331331$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tātaihia te 8 mā te pū o 6, kia riro ko 262144.

$$a\times \frac{1-\frac{1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Me tahuri te 1 ki te hautau \frac{262144}{262144}.

$$a\times \frac{\frac{262144}{262144}-\frac{1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Tā te mea he rite te tauraro o \frac{262144}{262144} me \frac{1}{262144}, me tango rāua mā te tango i ō raua taurunga.

$$a\times \frac{\frac{262144-1}{262144}}{1-\frac{1}{3^{2}}}=2457$$

Tangohia te 1 i te 262144, ka 262143.

$$a\times \frac{\frac{262143}{262144}}{1-\frac{1}{3^{2}}}=2457$$

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

$$a\times \frac{\frac{262143}{262144}}{1-\frac{1}{9}}=2457$$

Me tahuri te 1 ki te hautau \frac{9}{9}.

$$a\times \frac{\frac{262143}{262144}}{\frac{9}{9}-\frac{1}{9}}=2457$$

Tā te mea he rite te tauraro o \frac{9}{9} me \frac{1}{9}, me tango rāua mā te tango i ō raua taurunga.

$$a\times \frac{\frac{262143}{262144}}{\frac{9-1}{9}}=2457$$

Tangohia te 1 i te 9, ka 8.

$$a\times \frac{\frac{262143}{262144}}{\frac{8}{9}}=2457$$

Whakawehe \frac{262143}{262144} ki te \frac{8}{9} mā te whakarea \frac{262143}{262144} ki te tau huripoki o \frac{8}{9}.

$$a\times \frac{262143}{262144}\times \frac{9}{8}=2457$$

Me whakarea te \frac{262143}{262144} ki te \frac{9}{8} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$a\times \frac{262143\times 9}{262144\times 8}=2457$$

Mahia ngā whakarea i roto i te hautanga \frac{262143\times 9}{262144\times 8}.

$$a\times \frac{2359287}{2097152}=2457$$

Me whakarea ngā taha e rua ki te \frac{2097152}{2359287}, te tau utu o \frac{2359287}{2097152}.

$$a=2457\times \frac{2097152}{2359287}$$

Tuhia te 2457\times \frac{2097152}{2359287} hei hautanga kotahi.

$$a=\frac{2457\times 2097152}{2359287}$$

Whakareatia te 2457 ki te 2097152, ka 5152702464.

$$a=\frac{5152702464}{2359287}$$

Whakahekea te hautanga \frac{5152702464}{2359287} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 189.

$$a=\frac{27262976}{12483}$$